The Trotters could even afford to shrug off a missed Anelka penalty and still claim a second successive league triumph at the Reebok Stadium following their shock victory over Manchester United a fortnight ago.
Anelka atoned for the error by tapping home in the last minute - and with old stagers Kevin Nolan and Kevin Davies also among the scorers, Megson is swiftly becoming a worthy successor to the legacy left by Sam Allardyce.
• We must cut out mistakes - Bruce
There may still be a few remaining dissenters. But regular chants of 'Ginger Mourinho' were heard from the home fans, and Megson has certainly stabilised a situation that was deteriorating rapidly under Sammy Lee.
Of the two managers going head-to-head, it is Wigan boss Steve Bruce who has by far the most to worry about.
Middlesbrough's shock victory over Arsenal hardly helped Bruce, whose track record suggest Dave Whelan's money will be well spent when the transfer window opens next month. He faces an uphill battle to keep Wigan competitive before they get there, though.
What Bruce must eradicate before he can even think about dragging the Latics clear of trouble are the self-inflicted wounds that have marred his arrival the JJB Stadium.
Last week, a calamitous Titus Bramble blunder `gifted' Manchester City a 28-second lead. Today, Wigan lasted slightly longer - but there was still less than three minutes on the clock when Paul Scharner headed into his own net.
Quite why the Austrian did not pull out of his intended clearance when El-Hadji Diouf's cross floated over Anelka's head into a penalty area packed with Wigan players cannot be explained.
Instead - with goalkeeper Chris Kirkland ambling out to complete an easy catch, Scharner headed the ball into an empty net.
On the touchline, Bruce must have suffered a horrible feeling of deja-vu.
However, just as they did eight days ago, Wigan responded to the setback admirably - rolling up their sleeves, taking the fight to their opponents and deservedly drawing level.
There was a comical element to the Latics equaliser too as Abdoulaye Meite stuck out a foot to prevent Emmerson Boyce's low cross reaching Emile Heskey, only to see the ball roll perfectly for Denny Landzaat - who found the net in clinical fashion.
At that stage, Bolton looked to be there for the taking - their defence wobbling badly every time Wigan ventured forward.
Unfortunately for the visitors, they were unable to capitalise on the spirited foraging of Marcus Bent and should really have been behind midway through the half when Andreas Granqvist blocked Danny Guthrie's bouncing shot with an arm.
In such circumstances, Anelka is normally a man to be relied on. That was not so on this occasion, though, the French forward scooping a woeful spot-kick high over the bar.
Thankfully for Bolton's record signing, Nolan was able to spare his blushes before half-time.
It has not been an easy season for the Trotters captain. A one-time England candidate, Nolan was controversially axed by Sammy Lee earlier in the campaign.
Slowly, the Merseysider is recapturing his form - and the impudent way he flicked home the loose ball, after Granqvist had blocked Anelka's shot, suggested his confidence is rising too.
Three times at the start of the second period, Jussi Jaaskelainen was called upon to protect Bolton's lead.
Out of contract in the summer, Jaaskelainen proved his worth with a superb reaction save to deny Bent - having already repelled Heskey and Landzaat.
Heskey should have scored when he met Jason Koumas' cross with a firm header, although the same could also have been said about Diouf at the other end when Davies picked him out at the far post.
The outcome was still in the balance. But Davies removed any doubt when he completed an unhappy afternoon for Granqvist, getting on the wrong side of the Swedish defender to steer home Diouf's far-post cross from close range.
Anelka rounded off the scoring a minute from time, tapping in his ninth goal of a campaign that is suddenly looking full of hope for Bolton.
We must cut out mistakes - BruceWigan boss Steve Bruce has admitted his side must cut out basic individual errors if they are to stand any chance of staying in the Premier League.After a calamitous error by Titus Bramble gifted Manchester City a 28-second opener in Bruce's first game in charge last weekend, it was the turn of Paul Scharner to hand Bolton a perfect start at the Reebok Stadium.
With no home player attacking the ball, Scharner inexplicably headed El-Hadji Diouf's cross into an empty net as keeper Chris Kirkland was coming out to collect.
It left the Latics facing another uphill fight and while Denny Landzaat equalised, Bolton regained the initiative through Kevin Nolan's impudent back-heeled flick before Kevin Davies and Nicolas Anelka completed a 4-1 win.
Anelka could afford to miss a penalty and Bolton were still able to record their biggest win of the season, leaving Bruce immensely frustrated.
'You cannot play in this league and make individual errors like that,' said Bruce.
'We made an unbelievable one last week and have done the same again on Sunday.
'As a manager, the one thing you cannot account for are individual errors. You have to give yourself a chance and these mistakes are costing us badly.'
The defeat, coupled with Middlesbrough's surprise win over Arsenal and Tottenham's victory over Manchester City, means Wigan are now four points adrift of safety, with their top flight status in peril,
'It is not about other teams,' he said. 'We have to get our own results right.
'We have picked up one point from the last 10 games and if we are going to stay in this league, that has to improve.
'I always knew this job was going to be very difficult. It is a challenge but I am determined to try and put it right.'
After suffering a heavy defeat at Liverpool last weekend, victory was important for Bolton, who are slowly beginning to clamber their way out of trouble.
Typically, Nolan is leading from the front, putting early-season trauma, which at one stage saw the highly-rated midfielder axed by former manager Sammy Lee, well and truly behind him.
It was Nolan's quick thinking which allowed him to convert when Anelka's shot squirmed across goal after being blocked by Andreas Granqvist and manager Gary Megson could not have been more gushing about his captain.
'Since I have been here, Kevin has been an absolute credit,' he said.
'He sets the standard on and off the pitch. He is a leader in every sense of the word.
'Everyone can see he is desperate to win. He wants his team-mates to win.
'It is not just his goals, it is his work-rate. He is always one of the top three workers in terms of effort. The more of those you can have at a football club, the better you will be.'
Megson is still wary about Bolton's position which, while far brighter in terms of the league table, still leaves them only a point ahead of the drop zone.
'You want players to play with freedom but we are where we are,' he said.
'At one stage we were rock bottom. Now we are a few places higher but we are still not that far off being rock bottom.
'We have to keep trying to improve both our play and our results.'
Bolton Wanderers 4 - 1 Wigan Athletic
