Taruwar (109) and Mandeep (116) shared an unfinished 220-run innings between them for the third wicket to not only overhaul Odisha's first innings total of 205 but also take a crucial lead of 101 with still eight wickets in hand.
Earlier, openers Jiwanjot Singh and R Inder Singh begun Punjab's innings from an overnight score of 11 for no loss but the duo could add only 43 before DR Behera dismissed Jiwanjot with Natraj Behera taking the catch.
But Taruwar and Mandeep then took the onus on themselves and slowly and steadily build the platform for a big partnership.
Taruwar had 15 boundaries and one six in his 256-ball unconquered innings, while Mandeep hit 14 fours and a six in his unbeaten innings which came off 152 balls at the Punjab Cricket Association Stadium here.
Odisha 1st innings: 205
Punjab 1st innings: 306 for two in 94 overs (Taruwar Kohli 109, Mandeep Singh 116; Dhiraj Singh 2/44).