Pompey, who would have had victory sewn up at half-time if not for Benjani's air-shot from six yards after being presented with an open goal by a piece of Kanu magic, were unstoppable after the break.
They had been gifted a 10th-minute lead by Brynjar Gunnarsson's own-goal following a Mendes corner and Reading away with Kanu's header from a Sol Campbell cross after 52 minutes and a third from Mendes 14 minutes later.
• Harry hails 7-up Kanu
Reading, despite a brief show of defiance in the last 15 minutes of the first half when David James had to defy Bobby Convoy, could have suffered an even bigger trouncing but scored a consolation when Kevin Doyle stabbed home in an 85th-minute goalmouth scramble.
That was some sort of justice after Mendes got away with handling a Gunnarsson header on the line seconds earlier, but there was no comparison between the quality of the two teams on the day.
Kanu soon made his presence felt, wriggling clear to strike a low shot against a post in only the second minute, but referee Phil Dowd spotted the striker's arms around Ibrahima Sonko as they chased a through ball.
Just a minute later Pompey were close again through Gary O'Neil, whose first-time shot flew wide after Matt Taylor pounced on a smart backheel by Sean Davis to cross from the left.
O'Neil slanted in a cross from the right to set up Kanu's diving header straight at the relieved Marcus Hahnemann, but Reading were wilting under the pressure.
All this was in the first seven minutes as Reading struggled to get out of their own half and Portsmouth were finally rewarded three minutes later when Gunnarsson's own-goal gave them the lead.
Hahnemann should have prevented both corners which led to the goal, but when Mendes curled over an inswinger to the near post at the second attempt Kanu threw himself at it and missed, only for Gunnarsson's touch to turn the ball home.
On 17 minutes Steve Sidwell was left unmarked from a Bobby Convey corner, only to put his header too close to David James, who knocked it up in the air before scrambling it away.
Kevin Doyle was next to try his luck with a header two minutes later, flicking James Harper's cross over the bar.
But Reading had a huge escape almost immediately when Kanu nipped cleverly past Sonko and pulled the ball back, only for Benjani to connect with thin air in front of an open goal.
Benjani blotted his copybook again when falling dramatically in the area from Sonko's challenge and it was amazing referee Phil Dowd did not book him for diving.
Sidwell was just off target from distance, but Pompey required extreme bravery from James to keep their lead intact after he spilled a Doyle cross in the 32nd minute but then blocked Convey's follow-up fearlessly among flying boots.
Benjani, who took 15 games to register his first Pompey goal last season after a record #4.4million move from Auxerre, missed another sitter early in the second half.
He lobbed Hahnemann from O'Neil's through ball after James Harper made a mess of clearing, but the effort dropped just wide of a post.
It did not matter soon after when Kanu nodded in his seventh in nine games when Sol Campbell cushioned a volleyed cross straight onto his head in the 52nd minute.
Then midfielder Mendes rifled home off a post from the edge of the area after Doyle's header from an O'Neil corner dropped to the edge of the area in the 66th minute.
And after Mendes and Matt Taylor forced marvellous saves from Hahnemann, Pompey could have been ready to declare before Doyle's late consolation strike.
The result, and Arsenal's slip at home to Everton, lifted Pompey back to fourth in the Premiership, a fine 32nd birthday present for skipper Dejan Stefanovic, back in action after a knee injury.
Harry hails 7-up Kanu
Harry Redknapp hailed striker Kanu, who soared to the top of the Premiership's
scoring charts with his seventh goal in nine starts, as Portsmouth beat Reading
3-1.
Redknapp enthused: 'He's been fantastic.'
The Pompey chief snapped up the big Nigerian, 30, on a free transfer from West
Brom in the summer and the former Ajax, Inter Milan and Arsenal star has now
scored more goals this season than in the whole of the last two campaigns.
Redknapp said: 'Seven goals already is amazing. And he could easily have been
given our first one today as well.
'He has been superb. He keeps on heading the ball in and before I brought him
here I didn't think he could head it at all.
'But we played ever so well today and got at Reading straight away. I thought
it was going to be a difficult game because things seem to happen so often
against Reading in the opening minutes.
'We decided to go at them from the first whistle and it paid off with some
great football.'
Pompey's opener was a gift, with Reading's Brynjar Gunnarsson, under pressure
from Kanu, heading Pedro Mendes' corner into his own net - on his first
Premiership start - after 10 minutes.
Benjani Mwaruwari missed two glaring chances before Pompey wrapped up the
points with strikes by Kanu - a header from Sol Campbell's cushioned cross - and
Mendes - an 18-yard piledriver before Kevin Doyle's 85th-minute consolation for
Reading.
'I've seen Reading play a few times and they are better than this,'said
Redknapp, 'but we played really well today in every department.'
Pompey climbed into fourth place after a comfortable win and Reading boss
Steve Coppell admitted: 'They were better than us.
'The first goal was a sloppy one from our point of view but I was still
confident at half-time we could get back in it. Unfortunately it didn't work out
that way.
'We showed a lot more purpose at the end but you would have to say that
getting back from 3-0 down was always going to be difficult.
'We were up against a strong outfit, well-marshalled at the back, a
goalkeeper playing at the top of his game and powerful, competitive midfield.
Then there was Kanu's finishing - and it showed just how important he is after
they took him off.
'We got back into it then but it was too late.'
Coppell denied however that last week's 4-0 thrashing by Arsenal had destroyed
newly-promoted Reading's confidence.
He said: 'This was always going to be one of the most difficult games we
faced. It's like Manchester United, Chelsea and Arsenal. You are always happy if
you get something from them.
'We've looked at the fixtures ahead and if we can keep putting our best side
out I can guarantee we will be all right in this division. Pompey will
definitely be looking up this season rather than down.'
Only blot on Portsmouth display was Benjani's misses either side of half-time,
an air-shot at Kanu's cross in front of an open goal and a lob that fell wide of
a post after beating keeper Marcus Hahnemann.
But he was given a standing ovation when substituted by Andy Cole in the
second half and Redknapp said: 'Most players would be booed off after misses
like that but the fans here love Benji and so do I.
'He will run all day for you and he was great apart from the finishing. It
was a top performance by everybody.'
Portsmouth 3 - 1 Reading
