The striker, who scored 20 times for Almeria in Spain last season, wrapped up victory for Pep Clotet's side at St Andrew's.
Lukas Jutkiewicz's header had earlier given Blues the lead against a committed Barnsley side who lacked the quality to hurt their hosts.
It was a deserved win for Birmingham, their second of the season, as they moved up to eighth in the early Sky Bet Championship table.
Barnsley have four points from their opening four games to sit 17th after their promotion last term.
A tame Kristian Pedersen header after 13 minutes summed up a low key start.
The tenacious Tykes continue to adjust to life back in the second tier but never showed enough class and composure and, while Birmingham were hardly better, they did at least create two first-half chances.
Marc Roberts miscued his header from Fran Villalba's free-kick against his former club after 29 minutes.
Three minutes later Barnsley goalkeeper Samuel Radlinger was finally forced into action, tipping over Villalba's rising 25-yard drive.
It was a rare first-half chance as the two teams failed to find the right opening.
Barnsley at least emerged for the second half with more intent and Luke Thomas curled over 10 minutes after the break.
A breakthrough seemed unlikely when Radlinger just beat Jutkiewicz to a loose ball, before Blues scored two quickfire goals to win the game.
Clotet's men broke the deadlock after 69 minutes with Jutkiewicz's second of the season.
The lively Villalba found Wes Harding on the right and his deep cross was nodded in by Jutkiewicz from six yards.
Eight minutes later it was 2-0 as Barnsley were caught cold at the back.
Steve Seddon picked out the unmarked Gimenez and the £1.4million summer buy casually lobbed the onrushing Radlinger for his first Birmingham goal.
It wrapped up the points for the hosts, who gave Swansea loanee Jefferson Montero a second-half debut.