Interval substitute Ashton struck seven minutes into the second half as the Hammers made it four successive wins over Rovers to lift themselves into the top half of the Premier League.
Mark Hughes' side had the chances to at least clinch a draw, but after a run of seven successive league and cup victories, Rovers have now taken just five points from their last six games.
This was undoubtedly one of those cliched games of two halves as the first was instantly forgettable, followed by a barnstorming second.
• Green in the pink after Hammers win
The game was played at a typically high Premier League tempo, but the number of mis-placed passes and mistakes ruined the contest in the opening period.
It was soured at the start by Rovers fans proving they are unable to forgive or forget as they booed former star Lucas Neill with his every touch of the ball.
But as the opening 45 minutes wore on, those same supporters soon became bored with jeering the Hammers right-back.
Unfortunately, it was not the action on the field that distracted their attention as chances were few and far between courtesy of the fragility of both teams' forward play.
Too often moves broke down due to players failing to find a team- mate with an incisive pass when it was required most.
Instead, for the opening 30 minutes, all that warmed fans on a cold Blackburn evening were two long-range, yet close-shave efforts from David Dunn and Tugay.
Although Blackburn had appeared the more dangerous team early on, they surrendered that advantage due to those mistakes, much to the frustration of an animated Hughes in the technical area.
Scott Parker initially threatened by stroking West Ham's first chance a yard wide in the 34th minute with a dipping shot from 25 yards.
Then Nolberto Solano had two bites of the cherry in one particular counter-attack, but after his first drive was blocked, he flashed his second over the bar.
Blackburn swiftly responded, forcing Robert Green into the first notable save made by either goalkeeper as he turned aside a close-range strike from Morten Gamst Pedersen, with the winger in for the suspended David Bentley.
The game was in desperate need of an injection of vitality, and it arrived at the interval with Hughes replacing Aaron Mokoena with Robbie Savage.
That gave the midfielder his first taste of action since October 28 following a cartilage operation, but it was Hammers' substitute Ashton who made the immediate impact.
The 24-year-old striker, making his third sub appearance since recently returning from an ankle injury, was left unmarked in the 52nd minute to tap home his fourth goal of the season.
Solano fed George McCartney down the left wing and from the dead-ball line the left-back teased a low cross into the area where Ashton was free to score his first goal since September 26.
Mercifully, it led to the game opening up and so proving far more entertaining, with Green then pulling off a double save just five minutes later to preserve his side's advantage.
Green initially tipped away a downward header from Christopher Samba, and from the rebound he used his feet to deny Andre Ooijer at point-blank range.
That was followed 10 minutes later by Pedersen rifling an angled drive into the crowd from 12 yards when he should have at least hit the target from Roque Santa Cruz's through ball.
Following Green's heroics at one end, Brad Friedel responded in the 73rd minute with a sprawling stop to a Luis Boa Morte strike into the turf after meeting a Solano cross on the volley.
If West Ham should have been 2-0 up, Blackburn should definitely have drawn level soon after as Santa Cruz missed two chances in a matter of minutes.
The Paraguay international first flashed a header narrowly wide after rising to meet a superb left-wing cross from Stephen Warnock.
But then after delightfully controlling a cheeky dinked ball from Tugay, he drove his 15-yard shot over the crossbar with the goal at his mercy and as Green advanced.
Ashton then sidefooted over a Cole lay-off as the latter had taken advantage of an injury to Ooijer that led to the Dutch centre-back limping off and leaving Rovers down to 10 men for the last seven minutes.
Even then Blackburn came close to claiming a point, but for Green brilliantly pushing over the crossbar a Tugay volley from 30 yards that had flashed through a crowd of players.
Green in the pink after Hammers win
Robert Green reflected on a perfectly-executed gameplan as West Ham grabbed a 1-0 Premier League win at Blackburn on Sunday.Hammers goalkeeper Green was outstanding as his team dug in to defend the lead given to them by substitute Dean Ashton shortly after half-time.
'It is a tough place to come to. They have quality players now and are playing quality football,' Green told Sky Sports.
'To come here and put in the display we have and defended like that for the last 35 minutes is very good - excellent.
'Away from home we defend particularly well and hit teams on the break - and that is what we were looking to do on Sunday.'
Ashton, who came on as a second-half substitute as he continues his recovery from an ankle injury, described his goal as a 'bonus' to go with the fact he also finished another match in good health.
Manager Alan Curbishley, celebrating a year in charge of West Ham, congratulated his team on grinding out an appropriate result for him.
'There was great determination,' he said.
West Ham have a Carling Cup quarter-final at home to Everton on Wednesday - and with one eye already on that match, Curbishley was understandably heartened by on Sunday's win.
'Blackburn put a lot of pressure on us, but we dug in,' he added.
'We've come here and done a really good job. It is a massive week for us - that is the first leg.'
Rovers manager Mark Hughes admitted he could take few positives from his side's display, and claimed they only got going after falling behind.
'We never got anywhere near the level we are capable of - certainly in the first half our passing was poor and we never got any tempo or momentum to our play,' he said.
'They restricted us to playing in front of them.
'Second half, we were disappointed with the goal we conceded - possibly we needed that to get us going and after that we tried to ask questions of them.
'But it's one of those games we want to draw a line under.'
Blackburn Rovers 0 - 1 West Ham United
