Brian McDermott’s team battered away at the Barnsley goal in the second half but found goalkeeper Luke Steele in inspired form.
But the keeper could not prevent Manset from netting with 20 minutes remaining as the Frenchman finished from close-range to seal victory.
The win moves the Berkshire club to within three points of the top six.
The hosts, unbeaten in three, made three changes to the team that drew at Cardiff last week, allowing Huge Colace to make his first appearance since February.
McDermott was forced to tinker with the side that were knocked out of the FA Cup by Manchester City.
Ivar Ingimarsson, Brian Howard and Simon Church all came in as the Royals battled an ever-growing injury list.
It was Church who nearly opened the scoring with a shot that forced Steele into his first save of the afternoon.
Church was at the heart of the visitors’ best moves and he drove a shot wide of the upright as a both teams tussled for the upper-hand in the opening 20 minutes.
But Reading were by no means in control and the Tykes’ own front men were causing problems.
Marlon Harewood had a shot blocked by Ian Harte before his cross allowed Andy Gray to head on target, although Alex McCarthy pulled off a fine save to keep the scores level.
Boss Mark Robins brought on Martin Devaney in an attempt to inspire his side but it was McDermott’s team who looked sharper after the restart.
They slowly began to establish a rhythm that had the hosts on the back foot.
First Brian Howard, facing his former club, came within inches of rattling home a superb goal from distance until his shot was palmed away by Steele.
Steele then kept his team in the game by producing another save, this time to deny Shane Long as the striker’s first contribution of the afternoon was to nearly score.
Long and Howard then combined for the former to head over before Zurab Khizanishvili was denied by Steele’s athleticism as he tipped a powerful header over the bar.
Church fed Long for another opening but he was again unable to direct a header on target.
It turned out to be Church’s final contribution of the afternoon as McDermott brought on Manset in search of a goal.
And the substitute provided the breakthrough, taking just five minutes to make an impact as he linked up with Long to finish from close range.
That prompted a late bombardment from Barnsley, but Reading held out.