HAT-TRICK hero Ishmael Miller helped fire Albion into the FA Cup semi-finals for the first time in 26 years.
James Morrison opened the scoring in the 16th minute to set the Baggies on their way to Wembley as he scored in the quarter-finals for the second time in three years.
Miller added a second on the half-hour mark but League One Rovers gave themselves a lifeline when Danny Coles scored two minutes later.
However, where Fulham and Southampton had fallen on a difficult Memorial Stadium pitch in previous rounds, Albion proved too strong in the second half.
Miller notched his second of the game in the 69th minute and took his season's tally to 15 with his treble-strike five minutes from time. In between, 63rd-minute substitute Kevin Phillips bagged his customary goal within ten minutes of coming on as the visitors racked up five goals for the second successive round.
Jared Hodgkiss, who only returned from a hernia operation for the reserves on Wednesday, was handed his first start in 19 games in place of the injured Carl Hoefkens at right-back.
Mowbray made two other changes as Miller replaced the cup-tied Luke Moore in attack and Morrison started on the right wing, with Zoltan Gera dropping to the bench.
Rovers made a bright start and the Baggies needed Paul Robinson to block Andy Williams' shot on the edge of the box in the seventh minute.
Leon Barnett then hacked away Aaron Lescott's right-wing cross and the ball eventually found its way to Craig Disley, who screwed his 18-yard shot high and wide.
Miller picked up the ball and ran at the hosts' defence in the ninth minute before unleashing a 20-yard strike that deflected off David Pipe for a corner.
Three minutes later, Chris Brunt swung in a delicious cross from the left and Roman Bednar just could not get a big enough touch on the ball from six yards out to bundle it past Steve Phillips.
The fast and furious action continued when Disley got to the right by-line in the 14th minute but his back-post cross was just too high for Chris Lines.
A minute later, Robert Koren lofted the ball forward and Miller looked like heading it over Steve Phillips and into the empty net.
But the Rovers keeper managed to reach high enough to block the Baggies striker's effort and then quickly got to his feet to block Jonathan Greening's goalbound drive from the rebound.
But it was only a temporary reprieve as Brunt threaded the ball through to Bednar.
Steve Phillips could only parry the on-loan Czech hitman's low shot and Morrison thumped the loose ball home.
Four minutes later, Lines drifted a free-kick into the Albion penalty area which was flicked on for Rickie Lambert, who saw his point-blank volley well saved by Dean Kiely.
At the other end, Coles had to be alert to deny Bednar a simple tap-in from Miller's centre.
Martin Albrechtsen gifted the ball to Lambert in the 27th minute and his cross-cum-shot presented Williams with a golden opportunity to level - but he fired straight at Kiely.
Back came Albion and Brunt nipped inside Pipe on the left-hand edge of the box and smashed in a right-foot volley which Steve Phillips could only beat out.
The visitors doubled their lead on the half-hour mark. Miller latched onto a Koren ball down the right wing and held off Joe Jacobson before cutting inside and rocketing an unstoppable 18-yard shot past Steve Phillips.
A minute later, Barnett managed to recover to block Lambert's close-range effort.
But the Gas' persistence paid off from the ensuing 32nd-minute corner.
Skipper Stuart Campbell's centre was flicked on at the near-post and Coles stole in to score from inside the six-yard box.
The Baggies were still threatening and Lines prevented Morrison getting his shot away on the edge of the area in the 39th minute.
Three minutes later, Campbell burst past Greening and tried his luck with a 20-yard curling effort that drifted just past the right-hand post.
Miller looked sure to score a third for Mowbray's men in the first minute of stoppage time but as he tried to round Steve Phillips from Koren's throughball, he lost his footing and missed the chance to slot into an empty net.
Four minutes into the second half, Morrison swung in a cross from the right and Bednar nicked in ahead of Steve Phillips to flick the ball goalwards.
But Craig Hinton managed to clear off the line before Miller could react.
The wasteful Miller spurned another chance in the 52nd minute when he thrashed his shot well wide of the left-hand post with only Steve Phillips to beat after being put through by Koren.
Lescott's long throw-in managed to find Lambert in the box in the 61st minute and his shot deflected off a crowd of players and just wide for a corner.
Albion were then forced to weather two Rovers corners, just managing to scramble the ball away on both occasions.
Mowbray made a double change in the 63rd minute with Phillips and Gera replacing Bednar and Brunt respectively.
Albion took a stranglehold on the tie by snatching a 3-1 lead in the 69th minute.
Albrechtsen headed the ball forwards and as Coles tried to nod it back to his keeper he failed to see Miller, who was recovering from an off-side position, and the Baggies hotshot took full advantage by slotting home from 12 yards.
Four minutes later, Koren powered towards goal and Miller helped on his ball for Phillips to stab home from ten yards.
Jacobsen let fly with a 25-yard exocet in the 81st minute that beat Kiely and rebounded back off the left-hand post.
However, it was all going Albion's way and Miller completed his hat-trick five minutes from time as he coolly slotted Gera's pass into the bottom left-hand corner from just inside the area.
BRISTOL ROVERS (4-4-2): S Phillips; Lescott, Hinton, Coles, Jacobson; Pipe (Walker 72), Campbell, Disley, Lines (Haldane 55); Williams (Igoe 82), Lambert. Subs not used: Green (gk), Anthony.
ALBION (4-4-2): Kiely; Hodgkiss, Barnett, Albrechtsen, Robinson; Morrison (Kim 84), Koren, Greening, Brunt (Gera 63); Bednar (K Phillips 63), Miller. Subs not used: Danek (gk), Pele.
GOALS: BRISTOL ROVERS - Coles (32). ALBION - Morrison (16), Miller (30, 69, 85), K Phillips (73).
BOOKINGS: None.
REFEREE: M Clattenburg (Tyne & Wear).
ATTENDANCE: 12,011.
ALBION STARMAN: Robert Koren.
PIC: TWO GOOD...Miller smashes home his first and Albion's second
