Fryatt struck his second goal in three appearances for Hull since sealing a permanent move from Leicester on New Year's Day, converting a 66th-minute spot-kick after Tykes skipper Stephen Foster was adjudged to have pulled back the Tigers striker by referee Peter Quinn.
Quinn showed Foster a straight red card for a professional foul and Barnsley were reduced to nine men in the 90th minute when Jason Shackell was dismissed for a second yellow card offence.
Koren struck his sixth goal of the season in the 93rd minute when he slammed home Andy Dawson's cut back from 12 yards into the top corner.
Nigel Pearson's side created much the better chances and were good value for their sixth win in their last 10 Championship matches, with recent signings Fryatt, Aaron Mclean and James Chester all prominent.
Defender Chester, signed from Manchester United last week after an impressive loan spell at Carlisle, made his first appearance, while another recent signing Fryatt made his home league debut.
Barnsley midfielders Hugo Colace and Jacob Butterfield were both recalled to the starting line-up.
Tykes winger Adam Hammill was first to test either of the goalkeepers with a 20-yard shot which was comfortably held by Hull's Brad Guzan.
Barnsley goalkeeper Luke Steele made his first save in the 14th minute when Hull defender Anthony Gerrard latched on to a half-clearance to shoot on goal from 12 yards.
Mclean, making his first start for Hull since his move from MK Dons just over two weeks ago, then headed wide from Andy Dawson's corner and team-mate Nolberto Solano forced Steele into a better save in the 30th minute with an angled shot from inside the penalty area.
Hull almost made the breakthrough as half-time approached when Fryatt lashed in a shot from outside the area, but Steele, at full stretch, was equal to it.
Tykes midfielder Butterfield fired a warning soon after the restart, but his 20-yard effort drifted wide before Mclean was twice off target after trying his luck from outside the area.
Mclean was thwarted again by Steele in the 53rd minute after cutting in from the left to unleash an angled drive, and Koren almost broke the deadlock a minute later but his low shot came back off the post.
Hammill was proving the visitors' biggest threat, but Hull edged ahead in controversial circumstances in the 66th minute.
Fryatt was adjudged to have been pulled back by Foster in the area after turning his marker and stepped up to place his spot-kick beyond Steele.
Foster was shown a straight red card by referee Quinn for a professional foul and Barnsley played out the final 20 minutes with 10 men before Shackell departed to leave them with nine.
Hull wrapped up the points in stoppage time when Dawson crossed from the left and Koren smashed the ball high into Steele's top left-hand corner.