Hart, who played for England against Hungary on Wednesday, made six superb saves to keep City in the game before halftime. His team mates finally woke up to give Tottenham a contest after the interval.
In the end a draw was just about a fair result as City shaded the second half and both sides showed enough to suggest they will be serious contenders to finish in the top four, and possibly even in the mix for the title.
Chelsea, who won the league and FA Cup double, begin their season later at home to West Bromwich Albion while Manchester United, runners-up last season, must wait until Monday to open their campaign against Newcastle United.
Tottenham and City were involved in an absorbing scrap for fourth place last season, a fight Tottenham finally won thanks to a 1-0 win at Eastlands in May.
Harry Redknapp's side were the more cohesive unit on Saturday as they clicked straight into their old rhythm. They could have been out of sight before halftime as Roberto Mancini's rich side played the opening half at half pace.
City, who have spent more than $156 million in the transfer market since finishing fifth last season, gave debuts to Yaya Toure, David Silva and Aleksandar Kolarov, but it was Hart who kept them in the game.
As late as Friday, Mancini said he had not decided whether Hart or Shay Given would start the season in goal for City. The Italian's eventual decision proved fully justified as Hart denied a rampant Tottenham in the first half.
His first reflex save to block Jermain Defoe's close-range volley was superb and minutes later he tumbled to his right to save a dipping volley from Tom Huddlestone.
CITY'S BIG NAMES STRUGGLE
With City's big names struggling to make an impact, Hart again produced heroics to claw away Benoit Assou Ekotto's deflected shot.
On the half hour mark Hart was finally beaten but Gareth Bale's skidding shot thumped the base of the post and Aaron Lennon's follow-up was blocked by Vincent Kompany.
Mancini grimaced on the touchline as his expensive side spluttered on the lush green turf. Whatever he told them at halftime had an impact and they were greatly improved in the second half.
Almost immediately Shaun Wright Phillips was sent clear by a scooped pass from Yaya Toure, but he was denied by a goal-saving tackle by Assou-Ekotto.
Wright Phillips made way for England winger Adam Johnson midway through the second half while Redknapp switched his strikers with Defoe and Peter Crouch replaced by Robbie Keane and Roman Pavlyuchenko.
Johnson made an immediate impact, bamboozling two Spurs defenders before the ball broke for City's workaholic skipper Carlos Tevez whose shot was deflected just wide.
Pavyluchenko tested Hart with two low drives but Gareth Bale wasted the best chance of the game when he scuffed a shot wide with the goal gaping late on.
Later on Saturday Blackpool make their Premier league bow at Wigan Athletic, their first top flight match since 1971, while Aston Villa, stunned by the resignation of manager Martin O'Neill earlier this week, host West Ham United.