Zoltan Gera's first-half header was cancelled out by a controversial Iain Hume goal, before Craig Beattie secured the points for West Brom two minutes from the end.
Darren Kenton came to City's rescue on eight minutes when he nicked the ball away from Felipe Teixeira as the Albion striker threatened to break free for a clear run on goal.
The early stages continued to belong to the visitors who sought to get behind City down both flanks.
But the home side hit back on 20 minutes when an under pressure Luke Steele was forced to punch away a Stephen Clemence free-kick before Carl Cort had a shot blocked by Leon Barnett.
On the half-hour mark, Gera got the better of Joe Mattock but could only manage a shot into the side netting from a tight angle.
But Gera did much better a minute later when he arrived unmarked at the far post to head a Chris Brunt cross beyond the reach of Marton Fulop.
Patrick Kisnorbo then headed over after Richard Stearman had directed Clemence's free-kick back across the face of the goal.
Steele, making his Championship debut for Albion, ensured his side reached half-time in front when he dived acrobatically to scoop away Kisnorbo's goal-bound header from another dangerous free kick by Clemence.
Jonathan Greening was the pick of the midfielders on show and his eye-catching performance was almost rewarded when he sent a dipping shot just over after he had created space for himself with a jinking run.
After Roberts Koren had seen a shot deflected over, it was City who conjured up an unexpected leveller on 75 minutes.
Steele and Hume challenged for the ball after a huge punt by Fulop had bounced on the edge of the six-yard area.
As the two players tangled, the ball ended up in the back of the net with the City striker claiming the vital touch.
The leveller lifted Leicester who then had a penalty waved aside after Cort was bundled over by Barnett and then Steele needed two attempts to smother Mattock's stinging drive.
But two minutes from the end, Albion hit back with a superb winner when Beattie escaped the attentions of Stearman to curl an exquisite shot over Fulop and into the top far corner of the net.