Ruud van Nistelrooy put his domestic suspension to one side with four goals in the Champions League.
An awful backpass from Jiri Homola put the striker through for his first and he made it two from the penalty spot after a foul on Paul Scholes.
Lukas Zelenka finished a great move to pull one back for Sparta.
But Van Nistelrooy hooked the ball home for his third and tapped home close to full-time while Karel Poborsky was sent-off with four minutes left.
The Dutch international was a notable absentee as United went down at Portsmouth in the Premiership on Saturday.
And he underlined his worth to his team with four goals against the side who drew 0-0 with United in Prague two weeks ago.
Van Nistelrooy was one of four changes from the team that lost at Fratton Park, with Roy Keane, Liam Miller and Wes Brown also drafted in.
But it was a far from convincing performance, with the visitors thwarted on numerous occasions by goalkeeper Roy Carroll.
Former United midfielder Poborsky underlined Sparta's attacking threat after just two minutes.
The home defence sat off as the veteran cut in from the right and, after a neat one-two, Poborsky shot narrowly over Carroll's goal from 20 yards.
Just a couple of minutes later, only the woodwork prevented United from opening the scoring.
Van Nistelrooy's deep cross ran across the Sparta box and was met by a thunderous half-volley from Gabriel Heinze, whose shot crashed against the post and rebounded to safety.
Tomas Jun wasted another good chance for the visitors, shooting wide from 10 yards after snatching at the ball, before Wayne Rooney forced a decent save from Jaromir Blazek.
But it was Homola's horrendous backpass that led to United's opener.
The Sparta defender blindly passed towards his keeper and only succeeded in picking out Van Nistelrooy, who was ambling back onside after an attack broke down.
The Dutch international - in yards of space - closed in on goal before slotting home.
Scholes headed wide from short range, but made amends shortly after when Martin Petras' ungainly lunge at him resulted in a penalty for the home team that Van Nistelrooy converted.
Despite falling two behind Prague continued to cause problems and Carroll made a string of good saves.
First he denied Poborsky and then, on the stroke of half-time, made a brilliant double save to thwart Jun and Lukas Zelenka.
United immediately broke upfield and Cristiano Ronaldo, with a free run at goal, should have scored but could find no way past Blazek.
Ronaldo's failure to score a decisive third was punished six minutes after the break.
Zalenka's superb stepover wrongfooted the United defence and he continued his run towards goal, collecting a sharp pass from Jun before shooting past Carroll.
But their fightback was short-lived.
An optimistic long ball up field from Gabriel Heinze was poorly dealt with and Van Nistelrooy showed a predator's instinct to nip in and guide the ball past Blazek to complete a superb hat-trick.
Prague felt they should have been awarded a penalty when Roy Keane appeared to bring a player down but the referee waved play on.
Poborsky was dismissed after picking up two yellow cards and, on the stroke of full-time, Van Nistelrooy completed an unforgettable evening, tapping home from short range.
Man Utd: Carroll, Gary Neville, Ferdinand, Brown, Heinze,
Miller, Keane, Scholes (Phil Neville 69),
Ronaldo (Kleberson 69), Rooney, van Nistelrooy.
Subs Not Used: Howard, Saha, Giggs, Smith, Djemba-Djemba.
Booked: Miller, Brown.
Goals: Van Nistelrooy 14, 25 pen, 60, 90.
Sparta Prague: Blazek, Pergl, Homola, Kovac, Petras, Sivok,
Vorisek (Meduna 72), Poborsky, Zelenka, Urbanek (Simak 81),
Jun (Pacanda 81).
Subs Not Used: Bicik, Michalik, Cech, Koubsky.
Sent Off: Poborsky (87).
Booked: Poborsky, Homola.
Goals: Zelenka 53.
Ref: Alain Hamer (Luxembourg).