The visiting goalkeeper Josh Griffiths had to make a quick save in the beginning of the match to deny Barry Cotter's powerful 20-yard shot.
Adam Phillips then went close for the hosts, heading narrowly wide after meeting a corner from Keillor-Dunn.
Keillor-Dunn struck the opener in the 11th minute with a fine finish after latching onto a neat flick from Luca Connell.
Marc Roberts went close to putting Barnsley further ahead with a header which was tipped over by Griffiths, but Ruel Sotiriou equalised for Rovers in the 37th minute after capitalising on a defensive error.
TrendingBarnsley regained the lead after 65 minutes when Phillips found the net with a close-range header from Cotter's cross.
Keillor-Dunn went in search of his second goal of the afternoon, receiving a flick-on from Sam Cosgrove before a last-ditch tackle cut his run short.
Connell saw a 20-yard free-kick deflected wide in the closing stages.