Jennings repaid the selectors' faith after a torrid summer, digging deep to reach his second hundred in England colours as the hosts moved their lead past 350 at Galle.
The left-hander's 100 not out in 231 balls was not a pretty or dynamic knock but it was relentless in its hunger and concentration, qualities England will need plenty of in the post-Alastair Cook era.
Jennings hit a century and a fifty in his first two Tests, both in India, and once again found the sub-continental conditions to his liking as he watched Sri Lanka's spinners carefully and relied on frequent sweeps, both orthodox and reverse.
That he got over the line with a nudge for one was fitting, the 59th single of the innings. Ben Stokes, by contrast slammed three sixes in an entertaining cameo, but fell for 62.
England started the day 177 in front, and went on to score 73 for three in the two hours to lunch – a roughly even equation.
Jennings gritted his teeth and held his end up, happy to nudge his side towards a winning position rather than attempt anything outside of his comfort zone.
It brought him a modest 34 runs in the session, with a solitary boundary, but also saw him outlast three partners.
Rory Burns was the first, run out by Dimuth Karunaratne after embarking on overly eager single after getting tied down by spin.
Following a soft dismissal for nine in his maiden knock he will perhaps see his Test debut as a missed opportunity, though there should be plenty more to come.
Moeen Ali avoided a pair but did not linger, desperately hacking Dilruwan Perera to mid-on for three attempting to up the ante.
Joe Root was the key wicket and retiring hero Rangana Herath claimed it for the second time in the match, gripping the surface and taking the edge as the captain pushed forward.
Jennings had his only slice of luck late in the session, surviving an lbw shout on 58 that would have been given out on review had one been called.
England took full control between lunch and tea, adding 101 more runs against a tiring attack with Stokes strolling through the gears and clearing the ropes with three sweet strikes.
He briefly threatened to overtake his partner, who was sticking steadfastly to his chosen method. Perera ensured that would not be the case, pitching one outside leg and clipping the top of off as Stokes tried and failed to cover the spin.
Jennings played out five balls on 98 before tea, but the wait did not knock him off his groove and he safely strolled through for two more runs after play resumed.