The diminutive 24-year-old Argentinian striker opened the scoring in the 36th minute of a game littered with defensive errors but containing some superbly sharp quick-touch football from United.
The evergreen Ryan Giggs, who was 35 last Saturday, fired in a wickedly curling free-kick from the edge of the Blackburn box.
Tevez connected with the ball four yards out on the far post and it went into the net off Blackburn midfielder Aaron Mokoena.
Tevez also played his part in United's second goal four minutes later. Nani cut in from the left to play a neat one-two with Tevez before scoring with a 12-yard right-foot shot.
Blackburn boss Paul Ince brought on Benni McCarthy for Brett Emerton at the start of the second half and the South African was on the scoresheet three minutes later.
McCarthy beat Gary Neville in the air just outside the United box and was first to the ball as it dropped to score with a crisp right-foot shot from 12 yards out on the right side of the penalty area.
But it was United that looked to have sealed their semi-final place two minutes later. Giggs found Tevez on the right side of Rovers' box and, as he tried to go past Andre Ooijer, the Dutch defender brought him down.
Tevez stepped up to send Blackburn keeper Paul Robinson the wrong way as he placed the resulting penalty into the bottom left-hand corner.
United extended their lead four minutes later with another superbly worked goal.
Anderson and Giggs exchanged passes as they cut through the centre of the Blackburn defence. Tevez then got in on the act, inter-passing with the Brazilian before stroking the ball home from close range.
United eased off and were made to pay for their complacency. With six minutes to go, McCarthy set up Matt Derbyshire, who scored from ten yards out.
Martin Olsson rattled a United post with a header and the hosts' nerves were fraying 60 seconds into four minutes of stoppage time when Derbyshire's cross from the right was steered home by McCarthy from six yards out when he beat Jonny Evans to the ball.
But Tevez injected some calm into the proceedings for United with a rasping right-foot volley after being picked out by Anderson's pass.