A goal from Paul Scholes on the hour, a minute after he had arrived as a substitute, followed by Dwight Yorke's sixth of the season, sealed United's win. John Aloisi's late goal was little consolation to Strachan who, having been described in Sir Alex Ferguson's recent autobiography as not being a man to your back on, turned his own back on his former manager at the final whistle, exchanging neither congratulations nor a handshake.
Whatever was said in private, the public display was as obvious as the gulf between the teams but, afterwards, both were complimentary about each others' teams.
"They're a top side, probably the best in the world," said Strachan. "They fought like tigers but we showed a good appetite, were the better side and could have won by more," said Ferguson.
None was better than the second goal. Scholes, collecting the ball in the inside-left position 30 yards from goal, turned and hit a perfect 50-yard pass to David Beckham lurking on the right wing. He took one touch to kill the ball, and a second to send it arrowing into the box, where Yorke rose to flick it inside the far post for his sixth of the season.
Unusually for a Manchester United game, the centre of attention was an opponent, Robbie Keane, but it was his elder compatriot, Roy, who featured in the chants of "Keano, there's only one Keano".
Next year Robbie may well be the only Keane playing in England, but Roy is not leaving quietly. He drove United forward, as usual not caring whether it was an Irishman, Scotsman or Moroccan who was being crunched by his challenges. With Nicky Butt, making his first league start of the season in tandem, United seized control of the midfield with quick, slick passing.
However, their finishing was not up to the customary standard. Yorke did strike the post when given space 22 yards out after 15 minutes but was well wide after 37 after Butt and Teddy Sheringham - preferred to Andy Cole - had set him up.
Coventry had their moments and, but for Denis Irwin's smart clearance, might have taken the lead shortly before the break as Steve Froggatt's dangerous cross flew towards Paul Telfer.
Their confidence growing, Robbie Keane nutmegged Berg and Mustapha Hadji cheekily walked the ball across midfield before attempting to skip by two red shirts. He was abruptly halted by Beckham, who was booked for his challenge.
The game changed when Ferguson replaced Butt, who was suffering double vision, with Scholes. Less than two minutes later Scholes sent the ball flying past Magnus Hedman's outstretched right hand, courtesy of Beckham's cross. The watching Kevin Keegan must have been impressed.
Yorke's header appeared to have settled the game but, 12 minutes from time, Aloisi provoked a late Coventry onslaught when he ran onto a pass from Robbie Keane to score a well-taken goal. But United always had enough.
Coventry City (4-4-2): Hedman; (Breen Konjic, 83), Shaw, Williams, Edworthy; Chippo, Hadji (Aloisi, 72), McAllister, Froggatt; Robbie Keane, Whelan (Telfer, 33). Substitutes not used: Strachan, Nuzzo (gk).
Manchester United (4-4-2): Van der Gouw; P Neville (Curtis, 79), Berg, Stam, Irwin; Beckham, Roy Keane, Butt (Scholes, 62), Giggs; Yorke, Sheringham (Cole, 72). Substitutes not used: Culkin (gk), Solskjaer.
Referee: A Wilkie (Co Durham).