Midfielders Henry and Olofinjana both struck in the second half to earn Wolves their first win in front of their own fans since the 3-1 victory against Southend on November 4.
Henry broke the deadlock with his second goal in successive home games after 52 minutes before Olofinjana ended Barnsley's resistance 13 minutes from time.
Wolves made hard work of seeing off the challenge of Barnsley as they were frustrated for long spells by the display of in-form goalkeeper Nick Colgan.
No one was more relieved than Darren Potter to see Henry and Olofinjana score. The on-loan Liverpool midfielder had squandered a golden chance to score his first goal for the club when he missed a 28th minute penalty.
Colgan, particularly in the first half, stood firm against a strong Wolves onslaught. But Barnsley, who have only won twice away from home this season, lacked any real menace up front as they slipped to another damaging defeat.
It followed hard on the heels of Saturday's 3-0 reverse at the hands of Sheffield Wednesday and was not the start that manager Simon Davey wanted 24 hours after being confirmed as the boss on a permanent basis following his caretaker spell in charge.
Wolves would have been out of sight by half-time but for Colgan. While the running of Daniel Nardiello did cause Wolves problems, Barnsley were generally on the back foot with skipper Paul Reid having to lead by example with a captain's display at the heart of the backline.
Colgan pulled off two saves in quick succession to deny Michael Kightly and Craig Davies with Neil Austin completing the escape with a goal-line clearance.
Barnsley briefly threatened with a Nardiello snap-shot and a drive from Sam Togwell before Potter, who had earlier hit the post, fluffed his big chance.
Referee Andy Woolmer had no hesitation in pointing to the spot after 28 minutes when Robert Atkinson hauled down former Barnsley winger Michael McIndoe. Potter confidently took the ball only to see his weak spot-kick turned away by Colgan.
Fortunately for Wolves, Henry proved to be far more clinical in front of goal - neatly steering the ball past Colgan after running on to a pass from Olofinjana.
Olofinjana then set the seal on Wolves' success, but only 60 seconds after a smart save by Matt Murray from Atkinson's header had prevented Barnsley forcing their way back on to level terms.
Michael Kightly and Craig Davies combined to set-up Olofinjana who had the simple task of side-footing the ball home from six yards.