But all that came after Adam Johnson's 33rd-minute strike and City endured a nervous finish to take all three points.
Tevez returned to lead the City attack as a knee injury ruled out Mario Balotelli only four days after his hat-trick against Aston Villa, one of four changes manager Roberto Mancini made to the side that won 4-0.
Ian Holloway made only one change to the Blackpool team that won 2-0 at Sunderland, with captain Charlie Adam returning from suspension in place of Elliot Grandin, who suffered a hamstring injury at the Stadium of Light.
Tevez should have scored after only 22 seconds as the match got off to a tremendous start.
Adam misplaced a backpass that went straight to the Argentinian, but he screwed his shot wide.
David Silva fired wide moments later, while Blackpool had a fantastic chance when Gary Taylor-Fletcher beat Aleksandar Kolarov to break into the box, only to pull his cross back behind the run of DJ Campbell.
Tevez was almost played in again by another sloppy Blackpool pass, but this time he was forced wide and his cross was headed away from Yaya Toure by Ian Evatt.
Silva was inches away from capping a fine move with the opening goal in the 20th minute, but his shot scraped the wrong side of the post from Tevez's cross.
Silva went just wide again when he hooked Craig Cathcart's header out of the air on the edge of the area before sending a half-volley just the wrong side of the post.
City had been failing to test Richard Kingson and Tevez was off target again when he blazed over after being played in by Toure.
But the breakthrough came in the 33rd minute when Taylor-Fletcher cleared a corner straight to Johnson, who sent a low shot through the crowd and past the unsighted goalkeeper.
Tevez then wasted the chance to make it 2-0 three minutes later as he sent a penalty wide left after Toure was clumsily brought down by Luke Varney.
Phillips then tested Hart, breaking from the halfway line before sending a shot through the legs of Vincent Kompany which the England goalkeeper pushed away from danger.
Toure was denied a brilliant solo goal as he raced from deep inside his own area, beating four defenders, before being denied by a fine challenge from Cathcart as he prepared to shoot.
Pablo Zabaleta came on for his 100th City appearance and immediately teed up Tevez to curl a shot just wide of the right-hand post. City then suffered a blow as Silva came off with a knee injury, replaced by James Milner.
Joleon Lescott almost played a suicidal backpass with Hart just winning the race against Campbell to clear.
Tevez then missed an unbelievable chance to score, racing clear and rounding the goalkeeper, only to slip in front of the open goal and allow Blackpool to recover.
It was clearly not Tevez's day and he missed another great chance when he directed Milner's pull-back wide from the penalty spot after breaking free of his marker.
That kept the pressure on City and Hart needed fingertips to push Neal Eardley's rising drive over the crossbar.
From the resulting corner, substitute Brett Ormerod saw his header touched over by the England goalkeeper.
Blackpool kept up the heat in the final minutes, but City, using some often desperate defending, hung on.
Man City 1-0 Blackpool: Match Report - view commentary, squad, and statictics of the game as it happened.