Carlos Mendes Gomes’ 107th minute penalty gave the Shrimps victory and will see them welcome a number of former Premier League clubs to the Mazuma Stadium next season.
One goal always looked likely to settle a nervy, energy-sapping match but it was Newport who had the better of the few clear-cut chances created.
There was a change on the bench, however, where John O’Sullivan returned from a hamstring injury to replace A-Jay Leitch-Smith.
For their part, Newport made one alteration from the starting line-up which saw off Forest Green Rovers.
Skipper Joss Labadie was back in central midfield, replacing Anthony Hartigan, while Kevin Ellison had to be content with a place on the bench.
Adams had warned in advance that the Wembley surface would be slower than the players might be used to and that was shown to good effect early on.
Both sides gave away possession as passes held up on the pitch, allowing their opponents to regather the ball.
The first example came in the second minute when Aaron Wildig caught out the Newport defence with a quick free-kick to Mendes Gomes down the right-hand channel.
However, there wasn’t enough pace on the ball and Mendes Gomes almost dragged it from behind him in shooting wide.
In contrast, Newport took the pitch out of the equation with Mickey Demetriou’s long throws giving them sights of goal.
The first came on 12 minutes when Shrimps keeper Kyle Letheren was beaten to the ball by Scot Bennett, who headed wide.
Another saw Demetriou opt to throw inside to the unmarked Josh Sheehan who advanced on goal, only for his shot to strike the offside Labadie.
They had another go just past the 20-minute mark, this time the ball dropping to Labadie whose shot was blocked and Sheehan’s follow-up making its way through to Letheren.
Padraig Amond saw a shot deflected behind before Morecambe fans paid their tribute to Christian Mbulu with a rousing round of applause after 34 minutes.
Eight minutes later and they almost took the lead through perhaps the unlikeliest of scorers.
After Morecambe won possession deep in the Newport half, Mendes Gomes slipped the ball to full-back Liam Gibson, whose shot beat King but was diverted behind by Liam Shephard.
Back came Newport and, in the first of three added minutes at the end of the first half, Bennett was allowed to advance on goal.
With the Morecambe defence backing off, Bennett’s shot hit Yann Songo’o and wrongfooted Letheren but, luckily for the Shrimps, drifted into the side netting.
Neither side made changes at the break, though Morecambe switched to three at the back with Songo’o dropping back from midfield to partner Nat Knight-Percival and Sam Lavelle.
However, it was Newport who had the first sight of goal two minutes in.
Labadie flicked the ball inside to Lewis Collins, whose shot deflected off Morecambe skipper Lavelle and was gathered at the second attempt by Letheren.
Mendes Gomes was forced into some emergency defensive work to deny Amond before Newport opted for a double change, introducing Hartigan and Ryan Taylor.
Moments later and Collins’ acrobatic effort sailed over the Morecambe bar as one goal looked increasingly likely to win the game.
The Shrimps chanced their arm with the midway point of the half approaching, Ryan Cooney’s swerving shot forcing King into an uncomfortable save.
Nevertheless, it was Newport who continued to look the more threatening with Lavelle blocking shots from Demetriou and Sheehan.
The latter’s effort was worked back inside to Shephard, whose curling shot was tipped behind by Letheren to keep the Shrimps on level terms.
Lavelle headed off target from Wildig’s corner before Ellison was introduced in the 86th minute to a chorus of boos followed by a chant in support of Adams.
Three minutes later and Sheehan sent an optimistic effort from distance well over the bar, moments before five added minutes were indicated.
Midway through those and Morecambe had Letheren to thank for keeping them on level terms, turning behind Ryan Haynes’ free-kick as extra time arrived with the game goalless.
Having brought on Brad Lyons with quarter of an hour remaining, the Shrimps were forced into another change at the start of extra time.
Wildig limped off, meaning O’Sullivan made his first appearance since their win against Oldham Athletic in mid-April.
It also brought another change in shape for the Shrimps as they reverted to a back four with Songo’o pushed back into midfield.
They had the first chance of extra time as O’Sullivan found Cooney, whose first-time cross was headed wide by Cole Stockton.
It was the last opportunity of the first 15 minutes which brought the best sight of goal - and should have seen Newport ahead.
Second-half substitute Nicky Maynard got away from Gibson and crossed for Labadie, who blazed over from close range.
Adams shook up his team again at the start of the second period, introducing Kelvin Mellor for Gibson and seeing his team awarded a penalty 35 seconds in.
Haynes was deemed to have sent O’Sullivan to the ground, referee Bobby Madley taking his time in pointing to the spot.
Newport protested the decision but Mendes Gomes kept his nerve and emphatically sent King the wrong way from the spot.
Priestley Farquharson volleyed over for Newport as they sought a way back into proceedings with time running out.
Three minutes were added, ramping up the tension further, but Adams’ players held out to secure a promotion that was a scarcely believable prospect nine months ago.
Morecambe: Letheren, Cooney, Knight-Percival, Lavelle, Gibson (Mellor 105), Songo’o, McAlinden (Lyons 75), Diagouraga, Wildig (O’Sullivan 90), Mendes Gomes (Kenyon 114), Stockton. Subs not used: Halstead, Davis, Pringle.
Newport County AFC: King, Shepherd, Bennett, Demetriou, Lewis (Taylor 62), Labadie, Sheehan, Dolan (Hartigan 62), Haynes (Farquharson 111), Amond (Maynard 80), Collins (Ellison 86). Subs not used: Townsend, Ledley.
Referee: Bobby Madley.
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