The visitors had a glorious chance to take the lead early on when Andy Reid's cross was met by Billy Sharp, but the striker's effort went just wide.
Barnsley punished Forest for that missed chance less than 10 minutes later courtesy of Marlon Harewood, who latched on to Jacob Mellis's ball before rounding the keeper and slotting home against his former club.
Forest hit back soon after, however, when Greg Halford fired past Ben Alnwick with the outside of his boot to level the sides.
The away side then took the lead after a quick breakaway allowed Simon Cox the time and space to net his third goal of the season.
Forest completed the turnaround minutes later when Chris Cohen fired past Alnwick to make it 3-1.
Barnsley could have clawed their way back into the match with a little over 20 minutes left but Lee Camp produced a fine save to deny Kelvin Etuhu.
Forest put the result beyond doubt soon after when Jermaine Jenas dinked the ball over the keeper to make it 4-1.
The result lifts Forest to sixth in the table, while Barnsley are down in 19th.