Tevez missed a first-half penalty and then two sitters in the space of five minutes after the break. But all that came after Adam Johnson's 33rd-minute strike.
Tevez should have scored after only 22 seconds. Charlie Adam misplaced a backpass that went straight to the Argentinian, but he screwed his shot wide.
The breakthrough came in the 33rd minute when Gary Taylor-Fletcher cleared a corner 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 Yaya Yaya Toure was brought down by Luke Varney.
Toure was denied a brilliant solo goal as he raced from inside his own area, beating four defenders, before Cathcart's challenge denied him. Tevez then missed an unbelievable chance to score, racing clear and rounding the goalkeeper, only to slip in front of the open goal.