United rested several big names but were too good for Rovers at Old Trafford with Argentine striker Tevez running the show in a 5-3 victory in the only all Premier League clash of the quarter-finals.
Tottenham, who beat Chelsea in the final last season, fell behind against Championship (second division) side Watford but hit back to win 2-1 at Vicarage Road.
Two second tier clubs pulled off surprise wins in Tuesday's quarter-finals. Burnley beat a youthful Arsenal 2-0 while Derby County beat Premier League Stoke City 1-0.
Tevez headed United into the lead from close range and Nani made it 2-0 before halftime.
Benni McCarthy gave Rovers hope early in the second half but Tevez replied from the penalty spot and then finished off a sweeping move in style.
Rovers mounted some late resistance with Matt Derbyshire and McCarthy making it 4-3 but Tevez completed a great individual display with a screamer in stoppage time.
Tottenham were struggling at Watford and trailed to a Tamas Priskin goal but they drew level seconds before the interval when Jermaine Jenas was tripped in the penalty area and Roman Pavlyuchenko converted the spot kick.
Darren Bent came off the bench to win it for Spurs in the second half with a shot that crept in at the near post.
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