Rovers, who had gone three Premiership games without a goal, scored three times in the second half to end a resilient Hammers display.
Paul Dickov, who was sent off in the reverse fixture in the opening day of the season, returned to the starting line-up with a man of the match performance and two well-taken goals.
Bobby Zamora had given the visitors the lead on the stroke of half-time, before a debatable penalty decision changed the course of the game.
Marlon Harewood restored parity for Alan Pardew's side with a well-placed header midway through the second half, before the flying Finn stepped off the bench to power home the winner
An unfamiliar looking Rovers side started brightly, with Dickov twice going close inside the opening 15 minutes. On 19 minutes, the visitors were dealt a cruel blow when Danny Gabbidon was stretchered off.
As he went up with Morton Gamst Pedersen for a header, in an attempt to prevent a corner, the Welsh defender was sent crashing into the advertising board and would play no further part.
The injury to Gabbidon, who was replaced by former Rover Christian Dailly, disrupted the flow of the game, as neither side registered a shot on goal for the remainder of normal time in the half.
But moments after the fourth official showed five minutes of time to be added on, the Hammers scored a breakaway goal.
Harewood was allowed to run almost 40 yards down the centre of the pitch, before he slipped the ball through to Zamora, who confidently tucked the ball past Brad Freidel under the covering challenge of Steven Reid.
But the disappointment of Rovers' first-half display was soon put to rest in an explosive two-minute spell shortly after the restart.
A long throw-in by Pedersen, which was flicked on by David Bentley at the near post and struck the arm of Thomas Repka with referee Mike Reilly pointing to the spot.
Dickov, who had looked Rovers' most likely scorer in the first half stepped up and calmly sent Roy Carroll the wrong way.
Moments later and following a neat interchange of passes, Pedersen found himself with time and space on the right wing.
The Norwegian's inviting cross eluded the entire Hammers defence, which allowed Dickov to steal in at the back post and slide home his second in as many minutes.
But just six minutes later, West Ham were back level. After a surging run, Yossi Benayoon slipped in Zamora on the left and the former Spurs striker picked out Harewood in the centre, who headed home the equaliser despite the best efforts of Robbie Savage on the line.
On 67 minutes, Savage, who had already struck the bar once, curled another free kick on to the woodwork, before Harewood almost raced clear to put the visitors back in front.
But with just a quarter of an hour to play, Kuqi smashed home the decisive third goal.
The Finnish international collected his own flick-on header, bustled his way through the Hammers defence and volleyed the ball past the helpless Carroll off the underside of the bar.
An explosive half of end to end action, which saw the visitors pick up six bookings, ended with a hard-fought victory for Mark Hughes' men - their seventh in ten games on home turf.
Man of the Match: Paul Dickov - The Scotland striker was a general nuisance to the Hammers backline throughout the game and gained good reward for his efforts with two goals.