Tranmere had struggled to make their man advantage count following Mark O'Brien's dismissal 90 minutes into the match, but Jennings popped up 120 minutes in at Wembley to secure Rovers back-to-back promotions.
Both teams had their goalkeepers to thank for producing big saves in normal time, though ultimately both sides lacked a cutting edge in the final third until Jennings converted from a Jake Caprice cross.
For Tranmere their five-year absence from the third tier of English football is over, while Newport - denied a strong penalty shout in normal time - have to prepare for another season of League Two football after falling just short.
The two sides defied the odds to reach the final and, on the back of their semi-final triumphs, both managers stuck with winning formulas by naming the same starting lineups.
There was little between the sides over the course of the regular campaign and that proved the case in a quiet first half in the English capital.
Eventual matchwinner Jennings also managed to get a couple of shots away, forcing Day into a routine stop from one of them, while David Perkins and Robbie Willmott had attempts from range dealt with at either end of the field.
Tranmere had a penalty rejected with 25 minutes of normal time left following Dan Butler's challenge on Morris in the box.
The Tranmere goalkeeper, who kept the most clean sheets during the League Two campaign, reacted brilliantly to push the ball onto the upright at his near post.
Newport were dealt a major blow in added time as skipper O'Brien was shown a second yellow card for halting the run of Norwood, moments after Amond had yet another penalty appeal turned down.
Despite the man disadvantage it was arguably the Welsh side who had the better of extra time, with substitute Keanu Marsh-Brown nearly catching out Davies at his near post and Amond getting a header on target.
Those near misses would come back to haunt Michael Flynn's men, however, as Jennings was picked out by Caprice in the six-yard box to settle a nervy contest right at the death.
NEWPORT (4-3-3): Day; Poole, O'Brien, Demetriou, Butler; Bennett, Sheehan (Bakinson 90'), Labadie (Dolan 72'); Amond, Matt (Azeez 103'), Willmott (Marsh-Brown 105')
TRANMERE (4-5-1): Davies; Caprice, Nelson (Buxton 115'), Monthe, Ridehalgh; Morris (McNulty 82'), Harris (Pringle 53'), Banks, Perkins, Jennings; Norwood