Current Reds manager Kenny Dalglish saw Martin Skrtel head his side in front five minutes into the second half.
But his predecessor, Roy Hodgson, was indebted to Brunt for initially levelling matters from the spot and then scoring the 88th-minute winner.
Albion were worthy of their victory and are now unbeaten in five Premier League games under Hodgson.
They had the game's most potent attacker in Peter Odemwingie while Youssouf Mulumbu anchored the midfield effectively.
Luis Suarez again showed flashes of his quality for the Reds but Andy Carroll had a quiet game after scoring his first England goal in midweek against Ghana.
Liverpool were the first to settle and almost went ahead after two minutes.
Carroll won a header from a Raul Meireles corner and the ball fell to Dirk Kuyt whose close-range effort was blocked by Scott Carson.
Kuyt was first to react to the rebound and his shot clipped the top of the bar.
Carroll appealed in vain for a penalty after a challenge by Baggies central defender Jonas Olsson.
Liverpool suffered a setback after six minutes when Glen Johnson pulled up with a hamstring injury when trying to close down Brunt.
He was replaced by Sotirios Kyrgiakos who went into the middle of the back four with Daniel Agger replacing Johnson at left-back.
Kuyt dragged a low shot wide after Suarez had turned the ball into his path.
Brunt tried to catch Jose Reina out with a low 35-yard free-kick but the keeper was alert to the situation.
Liverpool received another injury blow after 25 minutes when Agger hobbled off with what appeared to be a knee setback to be replaced by Danny Wilson in a straight swap at left-back.
Paul Scharner became the first player to be yellow carded after 27 minutes for a foul on Jay Spearing.
Carroll followed him into Martin Atkinson's notebook late after a challenge on Steven Reid inside the Baggies box.
Reina was brought into meaningful action for the first time to cling on to a Reid header from Brunt's deep free-kick.
Wilson was yellow carded after bringing down Odemwingie two minutes before the interval.
Albion began the second half brightly and Reina parried away a well-struck drive from Cox.
But Liverpool broke the deadlock after 50 minutes through Skrtel's second goal of the season.
Carroll won a corner after his shot on the turn was tipped over by Carson at full stretch but he was well beaten by Skrtel's header from the resulting cross by Meireles after he had outjumped Scharner.
Carson then had to be alert to block a swerving shot from Kuyt after he had ran unopposed into the Albion box.
The home side tried to regroup and Reina went down to hold Brunt's left-footed shot.
Then after 62 minutes Brunt brought Albion level from the penalty spot.
Kyrgiakos was adjudged to have brought down the impressive Odemwingie inside the box and Brunt sent Reina the wrong way from the spot.
It was the third goal of the campaign for the Northern Ireland international.
Odemwingie was a constant menace to Liverpool and Reina did well to turn aside a fierce drive.
Hodgson made his first substitution after 74 minutes with Marc-Antoine Fortune replacing Cox.
Liverpool skipper Jamie Carragher made a crucial block on Odemwingie's powerful shot.
Then Odemwingie flashed a shot across the face of goal after being found in space by Fortune.
A minute late Brunt put the Baggies ahead with his second penalty of the game.
Odemwingie shook off the challenge of Kyrgiakos and then was brought by Reina.
Up stepped Brunt to hammer the spot-kick past Reina.
Liverpool fought hard for an equaliser, but Carson made a superb save from Suarez before Nicky Shorey headed off the line from Suarez.