Two-goal Craig Bellamy shipwrecked the Pirates at the Memorial Stadium with a clinical first-half double.
But while the £7.5m striker secured Hammers third round place with his first-ever strikes for West Ham United, there was no Carling Cup cheer for fellow new signing Kieron Dyer, who was stretchered away with a suspected broken leg with just a dozen minutes on the clock.
And the midfielder's terrible injury is disastrous news for Alan Curbishley who paid the price for justifiably naming a strong side after coming into this tie declaring that he has always taken this competition seriously.
From Crewe Alexandra back in 1992 to Chesterfield last year, the Hammers had bowed out of this competition to lower league sides on no fewer than nine occasions during the past 15 seasons, a sorry sequence that the new manager wanted to halt.
And although Curbs' pre-match plans had been disturbed by the absence of Dean Ashton, whose partner was about to give birth, the Hammers' boss had still been able to field a powerful West Ham United line-up to face an unchanged Rovers side sitting in ninth-spot in Coca-Cola League One, following Saturday's 1-0 win at Oldham Athletic.
There were four changes from the team that drew with Wigan Athletic at the weekend as Danny Gabbidon, Luis Boa Morte and Lee Bowyer each came in for Matthew Upson, Matthew Etherington and Mark Noble, while 'keeper Richard Wright was handed his first start in place of Robert Green.
But after the unmarked Bobby Zamora nodded Boa Morte's cross over the bar in the opening seconds, Curbs was forced to make a further, unwelcome change on 12 minutes, when Joe Jacobson scythed through Dyer with a hefty touchline tackle that saw the England midfielder stretchered away with a suspected double fracture of the right leg, as the Pirate curiously escaped any more punishment than a free-kick.
With substitute Mark Noble slotting effortlessly into the central midfield berth vacated by the luckless Dyer, West Ham continued to spend more and more time in the Rovers' half as the team 40 league places below them relied on sporadic counter-attacks.
Apart from Jacobson's 20-yard free-kick that drifted wide of Wright's left-hand upright, the debutant 'keeper had enjoyed an incident free introduction to life between the West Ham goalposts.
And it was no surprise when Hammers took the lead on the half-hour mark through the unmarked Bellamy, who collected the ball from Hayden Mullins and turned towards goal before unleashing a thunderous, low 30-yarder that flew past the sprawling Steve Phillips.
Having netted his first goal for the club, the Hammers' striker might have had a second moments later, however he headed the impressive George McCartney's cross straight to the Rovers' 'keeper.
In reply, Richard Walker nodded into Wright's arms and Lee Bowyer denied Jacobson in the act of shooting, but with Rovers only showing token resistance, that man Bellamy did not have to wait too long to double his tally.
Seconds before the interval, the Welshman lengthened his stride as he raced across the West Country turf to slot Lucas Neill's cleverly lofted through-ball across the face of the exposed Phillips and into the far corner of the net from ten yards, to the delight of the 1,463 Hammers' fans packed amongst the 10,831 crowd.
Emerging for the second period with the job more than half-done, West Ham could have made it 'Game Over' in the opening exchanges when Noble played in the overlapping Bowyer but his tightly angled shot rolled agonisingly beyond the far post.
With nothing to lose, Rovers threw caution to the wind in a bid to claw their way back into the tie and Wright, suddenly on full alert, pulled off a fine double save to prevent a deflected Neill own-goal before recovering to claim Richie Lambert's follow-up header from under the bar.
A few more awkward scrambles in the Hammers' box proved the cue for James Collins to replace McCartney on the hour, while Paul Trollope introduced Andrew Williams, Lewis Haldane and Sammy Igoe at the expense of Craig Disley, Lambert and Jacobson.
Certainly, those three new faces put the wind in the Pirates' sails, for with 20 minutes remaining, Richard Walker's defence-splitting chip was collected by substitute Williams, who clipped the ball over the advancing Wright from 12 yards to give the League One side hope.
That set up an almost inevitable late onslaught that led to more Rovers' raids, while at the other end, only a goal-line clearance prevented Collins from booking the east enders deserved place in the third round draw long before the final whistle.