The Championship club led 1-0 at the break when Mifsud's looping volley deceived Brad Friedel in the Rovers goal.
Elliott Ward doubled the visitors' advantage from the spot after Leon Best had been brought down inside the box and Dele Adebola made the victory safe with a superb solo strike.
David Bentley restored some credibility for Mark Hughes' men with an effort from outside the box, before Mifsud scored his second of the game in time added on.
After a confident start by the visitors, Rovers soon got their passing game going.
On 13 minutes, Bruno Berner was upended right on the edge of the Coventry box and Bentley's low curling free-kick was parried by Dimi Konstantopoulos before Ward had to hack clear close to his own line.
Just past the quarter-hour mark, some neat one-touch football by the home side ended with Bentley floating over a cross for Maceo Rigters, but the Dutchman failed to direct his header on target.
Two minutes later, a quick Coventry break down the Rovers right saw Best play a clever back-heel into the path of Mifsud and the Maltese striker's crisply-struck shot was well kept out by Friedel.
Rovers' best chance of the half arrived on 29 minutes when Brett Emerton played the ball clean through to Benni McCarthy with the outside of his right foot.
The linesman's flag stayed down, but the South African striker blasted the ball straight into the goalkeeper's grasp.
But just five minutes later, the hosts found themselves behind.
A hopeful ball into the box dropped kindly for Mifsud and the man who almost single-handedly knocked Manchester United out of the Carling Cup hooked his shot over the head of Friedel and into the far corner of the net.
McCarthy twice tried his luck from distance as another first-half of football ended in disappointment for the home fans.
There was an improvement at the start of the second half as just four minutes in, Bentley's in-swinging free-kick almost caught out Konstantopoulos, but the Greek keeper just managed to tip the ball over the bar.
Chris Samba then twice struck the woodwork from the resulting plays.
Three minutes later, a Coventry corner was somehow headed over the bar by Adebola and straight up the other end, Rigters sliced his shot from Bentley's ball in.
Rovers made a double change as they looked to level the scores, but it was the visitors who netted next.
Jay Tabb unleashed a rocket onto the Rovers bar and as Best went for the follow-up, he was knocked to the ground by Zurab Khizanishvili and referee Lee Probert pointed to the spot.
Friedel had saved his last two spot-kicks, but he was powerless to prevent Ward from curling his effort into the top left-hand corner of the net.
Rovers responded well with Samba and substitute Matt Derbyshire both going close, before the visitors ought to have extended their lead.
On 77 minutes, Isaac Osbourne's cross was somehow glanced wide from the unmarked Mifsud, before Tugay's back pass went straight to Best, but after rounding Friedel, the former Southampton striker fired into the side-netting with the goal at his mercy.
However, with seven minutes remaining, the Sky Blues did add their third courtesy of a stunning solo strike from Adebola.
The much-travelled frontman powered his way past Khizanishvili, Morten Gamst Pedersen and Ryan Nelsen, before firing a low left-foot shot past Friedel.
Rovers grabbed a consolation two minutes later when Aaron Mokoena laid the ball off to Bentley, who drilled a long-range strike into the bottom left-hand corner of the net.
But as Hughes' troops pushed forward, Mifsud was left unmarked at the back and the pint-sized striker sealed the win with a crisp right-foot strike with 92 minutes on the clock.