Balotelli opened the scoring in the first half having combined with City skipper Carlos Tevez, who was back in the team following his two-match injury lay-off.
The Italian striker then converted David Silva's cross soon after to give the visitors - defeated in their last three matches - a two goal advantage.
Balotelli's afternoon took a turn for the worse after the break, though, when he was red-carded following a tangle with Youssouf Mulumbu, who was also sent for an early bath after scything down Tevez late on.
With Arsenal being defeated by Newcastle, the result meant fourth-placed City drew level on points with the Gunners in the Barclays Premier League.
It also meant the Blues overcame their hoodoo at The Hawthorns, where they had been beaten on their last four visits in all competitions - including a Carling Cup tie earlier in the season.
Given that and the recent struggles of Mancini's side, the Baggies had plenty of reasons to feel confident going into the match, and it was evident in the way they got started.
Chris Brunt ran on to a neat through-ball from Marc-Antoine Fortune after only a couple of minutes, with Kolo Toure making an interception which almost resulted in an own goal.
Moments later, Brunt curled in a shot that Vincent Kompany managed to block before Nigel de Jong picked up a yellow card for a blatant handball.
At the other end Balotelli, preferred as partner for Tevez in attack to the benched Emmanuel Adebayor, went down in the box under Marek Cech's challenge, but referee Lee Probert waved play on.
City were starting to impose themselves and Tevez's shot ricocheted off a West Brom shirt to Pablo Zabaleta, who fired over the bar.
Balotelli tried to find Tevez with a back heel just before the quarter hour mark and when he did claim possession, the skipper saw his effort deflect wide.
The link-up play was more effective in the 20th minute, though, as the visitors went ahead through Balotelli, the 20-year-old notching his first Premier League goal by sliding in to meet a cross from Tevez, who had latched on to Silva's incisive pass.
Silva had a chance to double the lead soon after but saw his attempt blocked by Scott Carson.
West Brom looked to respond quickly and Brunt delivered a useful cross which Fortune was just unable to get on the end of.
But having made the breakthrough, Balotelli took only six minutes to strike again and put City 2-0 up.
Silva was involved once more, lofting a pass to the former Inter Milan man who finished firmly despite the attentions of Gabriel Tamas.
The scoreline did not flatter City and they almost increased their advantage when Tevez sent a free-kick on to the roof of Carson's net.
Balotelli then caused uproar by bundling over Nicky Shorey, although Probert did not deem the incident worthy of a yellow card.
The City striker might have been presented with a chance to complete his hat-trick just before the break but Yaya Toure's cross was cleared away.
City continued to press as the second half got under way, with Jerome Boateng finding himself in an unusually advanced position and just beaten to the ball by Carson.
Simon Cox almost pulled one back for Albion in spectacular fashion, though, with a swerving effort that cracked against the post.
Having no doubt impressed watching Italy boss Cesare Prandelli with his finishing prowess, Balotelli then received his marching orders after being shown yellow and then red cards in quick succession.
The man advantage seemed to rouse the Baggies, who panicked City into hitting the ball against their own bar from a corner, before Joe Hart tipped Shorey's free-kick over.
Having been given fresh attacking impetus by the introduction of joint top scorer Peter Odemwingie - fit again after a knee injury - and Giles Barnes and roared on by their fans, the home side kept up the tempo, with Mulumbu and Brunt shooting too high.
But it was only in terms of players that they found themselves level with eight minutes of normal time remaining as Mulumbu was dismissed for a reckless lunge on Tevez - West Brom's third red card of the week after they were reduced to nine men at Blackpool on Monday.
Albion tried to remain on the front foot but could not find a way through as City made off with a morale-boosting three points.