Jennings was unbeaten on 98, having combined for 107 runs with Ben Stokes after England lost three wickets in the morning session on a day of relatively slow scoring.
After Stokes was removed, Jos Buttler had reached 14 at the other end with England primed to claim victory in the first match of a three-test series.
The tourists resumed on 38-0 with the openers consolidating their position until Rory Burns' foolhardy pursuit of a non-existent single culminated in his downfall.
Burns pushed Dilruwan Perera to mid-on and set off down the wicket, but could not beat Dimuth Karunaratne's direct throw and was dismissed for 23.
Moeen Ali's four wickets helped England take a 139-run first innings lead but the spin all-rounder could not justify his promotion to number three for the second time in the match.
He followed up his first innings golden duck with three, tamely hitting Perera straight to Rangana Herath at mid-on.
England captain Joe Root (three) also had a deja vu moment when Herath dismissed him for the second time in the match.
Playing his final test, left-arm spinner Herath drew the England captain out and bowled slightly wide to induce an edge that safely nestled into Niroshan Dickwella's gloves.
Jennings looked reasonably confident against the spinners, often playing the sweep shot -- both traditional and reverse -- to negate them. His composed knock included six hits to the fence.
Stokes shrugged off his early tentativeness to clobber three sixes in his 62 before Perara spun one past his bat to hit the top of the off-stump with a beautiful delivery.
(Reporting by Amlan Chakraborty in New Delhi; Editing by John O'Brien)
