It was the Argentina striker's third treble of his City career and took his tally for the season to 20 goals. He was given a standing ovation when he came off four minutes from time.
It was just the result manager Roberto Mancini was looking for as it came on the day a minute's applause was held in memory of former favourite Neil Young, who died recently after a long battle against cancer.
City almost took the lead in the fourth minute when West Brom defender Paul Scharner failed to cut out a cross from Aleksandar Kolarov.
Tevez was perfectly positioned and got in a first-time shot that beat goalkeeper Boaz Myhill but he saw it come back off the post.
Albion responded in the 12th minute. Chris Brunt delivered a well-struck free-kick on the edge of the area but goalkeeper Joe Hart diverted his effort to safety.
A minute later Hart was again forced into action, tipping a looping header from Jonas Olsson over the bar.
City made the breakthrough in the 17th minute with Steven Reid punished for barging Kolarov. Tevez sent Myhill the wrong way from the penalty spot.
Tevez extended their lead in the 22nd minute after skipping into the area following a one-two with David Silva before finding the corner with his effort.
West Brom continued to be pegged back and Olsson did well to block Silva's path to goal in the 31st minute after he had linked up with Yaya Toure.
A minute later Myhill reacted superbly to get the slightest touch to a Kolarov thunderbolt and touch it onto the bar.
City continued to turn the screw and Silva made space for himself in the area only to see his shot beaten away by the goalkeeper.
Tevez completed his hat-trick in the 36th minute with his second penalty of the game.
Jerome Thomas, for reasons only known to himself, handled in the area and referee Martin Atkinson had no hesitation in pointing to the spot.
Tevez stepped up and this time sent his effort high over Myhill to make it 3-0 to City.
The skipper came close to adding a fourth in the 42nd minute after being set up by Silva but the ball went the wrong side of the post.
However, West Brom almost pulled a goal back two minutes into the second half when Peter Odemwingie scampered forward only to see his effort turned away at the post by Hart.
Then Marc-Antoine Fortune squandered a good opportunity for the visitors, finding the side-netting from a good position.
West Brom again pushed forward and Hart had to be alert in the 71st minute to turn away a free-kick from Nicky Shorey 20 yards out.
Tevez should have scored his fourth of the game eight minutes later when he was set up by Gareth Barry.
Given how prolific he had been in the match there were gasps of astonishment around the ground when he spooned the ball over the bar from six yards.
Substitute Shaun Wright-Phillips was then denied by Myhill on the stroke of full-time as City secured their first win in four games.
West Brom, however, remained in deep trouble and locked in a relegation battle after further defensive slip-ups.