Just seven minutes after his arrival at the start of the second half, the England striker tapped home the game's only goal from George McCartney's cross.
Roque Santa Cruz missed two glaring chances for the home side, who slipped to their third defeat in five.
Before the game, Rovers manager Mark Hughes made one change to the side that defeated Newcastle 3-1 at Ewood Park eight days ago, with Morten Gamst Pedersen recalled for the suspended David Bentley.
Hammers boss Alan Curbishley stuck with the same eleven that lost 1-0 away to Chelsea - a team which included former Rovers skipper Lucas Neill, who was booed throughout.
Shots from distance appeared to be the order of the day for the home side early on.
In the fifth minute, Benni McCarthy fed the ball through to Santa Cruz, who laid it off to David Dunn, but the Blackburn-born midfielder's long-range effort grazed the top of Robert Green's bar.
Just past the quarter-hour mark, Tugay let fly from fully 30 yards, but his stunning strike swerved just past the upright.
Pedersen was next to try his luck with a shot that deflected well wide and, from his resulting corner, Andre Ooijer headed narrowly over.
Not to be outdone, Scott Parker, who saw plenty of the ball in an altogether disappointing first half, which lacked creativity and width, fired a dipping right-foot shot inches wide of Brad Friedel's right-hand post.
On 40 minutes, twice Stephen Warnock switched off, but twice Nolberto Solano failed to make him pay and, at the other end, Dunn lifted the ball over the top to Pedersen, but the Norwegian's left-foot strike could only find the side-netting.
Both sides made changes at the break, with Robbie Savage coming on for Aaron Mokoena and Ashton replacing Matthew Etherington to add extra fire-power for the visitors.
And the Hammers substitution paid immediate reward. Just seven minutes after the restart, Rovers failed to clear their lines, with Brett Emerton twice losing possession, and McCartney drilled the ball across from the left for Ashton to side-foot home.
Rovers responded well, with Chris Samba heading straight at Green from a corner while Ooijer was denied by the England keeper on the follow-up at his near post.
The home side were enjoying plenty of the ball and, on 66 minutes, Dunn slipped in Pedersen, but again the winger fired wide of the mark.
Luis Boa Morte almost doubled the visitors' lead on 73 minutes, but his fiercely-struck volley from Solano's deep cross was well kept out by Friedel, before Santa Cruz had two golden opportunities to draw level in the space of as many minutes.
Firstly, Pedersen swung in a cross from the left and the Paraguay striker sent a towering header wide of the target.
A little over 60 seconds later, Tugay cleverly lifted the ball over the West Ham defence, Santa Cruz's control was first class, but his finish was woeful - blazing high over the bar.
Ashton then had an equally embarrassing miss from Carlton Cole's centre at the other end, before Green secured the points for Curbishley's side with a superb reaction save from Tugay's bullet strike through a crowd of players.