The England right-back put through his own net in the 22nd minute, rushing back in an attempt to prevent Wayne Rooney taking aim from Ashley Young’s cross and succeeding only in scuffing the ball into his own net.
United handed competitive debuts to Sergio Romero, Matteo Darmian, Morgan Schneiderlin and Memphis Depay, while Bastian Schweinsteiger came on in the second half to become the club’s first German player.
“The first time you play at Old Trafford is always difficult, but I liked the performance, especially of Darmian,” United manager Louis van Gaal, who was celebrating his 64th birthday, told BT Sport.
On goalkeeper David de Gea, dropped amid interest from Real Madrid, Van Gaal added: “He is our best player for the past two seasons, chosen by the fans, so we can’t let him go so easily.”
Spurs made a bright start in the Salford sunshine, Christian Eriksen volleying over from Harry Kane’s scooped pass, but they retreated into their shells following Walker’s moment of misfortune.
United failed to take full advantage, however, with Young the only player to muster a shot on target, and Eriksen forced Romero — deputising for De Gea — to make two sharp saves in the latter stages.
Chelsea launch their title defence at home to Swansea City later on Saturday.
Leicester City found themselves on top of the table after Algerian winger Riyad Mahrez inspired them to a 4-2 home win over Sunderland at the King Power Stadium.
After Marc Albrighton teed up Jamie Vardy for an 11th-minute header, Mahrez scored with a header from another Albrighton cross and then added a penalty to put Leicester 3-0 up with only 25 minutes gone.
Cabaye strikes for Palace
Jermain Defoe and Steven Fletcher found the net for Sunderland in the second half, but a smart strike by Albrighton kept Leicester in control.
Watford fared the best of the three promoted clubs, drawing 2-2 with Everton at Goodison Park.
But they twice squandered the lead, with goals from Miguel Layun and substitute Odion Ighalo cancelled out in turn by Ross Barkley and Arouna Kone.
The first top-flight game in Bournemouth’s 116-year history ended in a 1-0 home defeat against Aston Villa, who prevailed courtesy of a 72nd-minute header from their new striker Rudy Gestede.
“It was a really good performance from us. I can’t be too critical,” said Bournemouth manager Eddie Howe, whose side won the Championship last season.
“I’m disappointed with the defeat, but looking forward to the rest of the season.”
Norwich City, promoted via the play-offs in May, lost 3-1 at home to Crystal Palace.
Wilfried Zaha and Damien Delaney put the visitors in charge before substitute Nathan Redmond hit back for Norwich, but Palace’s star recruit Yohan Cabaye sealed victory in stoppage time.
Arsenal host West Ham United and Liverpool travel to Stoke City on Sunday, with last season’s runners-up Manchester City opening their campaign at West Bromwich Albion on Monday.