At stumps, Karnataka, who bowled out Gujarat for 210 were 280 for six.
Overnight 61 without loss, Karnataka were dealt three blows in a single over by Trivedi before Barrington's painstaking ton helped them take a crucial 70-run lead.
Trivedi's first prey was captain J Arun Kumar, who was unbeaten on a fiery 40 off 43 balls. The batsman gave an outside edge to keeper Nilesh Modi.
The lanky paceman again struck in the same over, removing young Robin Uthappa, caught by Gujarat skipper Mukund Parmar at first slip.
Wicketkeeper V Tilak Naidu also followed, and very soon, there were four Karnataka batsmen cooling their heels in the pavilion after Shyamal Bhatt trapped an aggressive Vijay Bharadwaj in front of stumps with the total on 84.
But Rowland, who smashed his seventh Ranji century and second of the season, played cautiously and put on 83 runs for fifth wicket with Deepak Chougule (37) to reconstruct the innings.
His 122 came off 320 balls with seven boundaries after 426 minutes at the crease. Stuart Binny also chipped in with a useful 41 before being run-out by keeper Modi.
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