The Southampton striker came off the bench to net the deciding goal with his first touch of international football on Wednesday night, with the Three Lions twice coming from behind
The Southampton forward headed home a corner with his first touch after coming on as a second-half substitute to hand the hosts victory in the first meeting between the bitter rivals in 14 years.
James Morrison and Kenny Miller had twice given the Scots the lead earlier in the match, only for Theo Walcott and Danny Welbeck to cancel out the visitors' advantage.
Lambert's goal provided a fitting end to a fabulous contest, which saw England avenge their 1999 defeat to the Tartan Army at Wembley.
Roy Hodgson named a strong side for the encounter, making the most of a rare opportunity to field Jack Wilshere alongside Steven Gerrard in midfield while Wayne Rooney ended all doubts about his injury status by starting up front.
The game certainly started in a confrontational manner, with the booing of national anthems setting the scene for some feisty early tackles in an intense opening.
England eventually carved out the first real chance among the melee, though Rooney could only scuff Leighton Baines' cross from the left beyond the far post.
Scotland made them pay for that miss with just 11 minutes on the clock, as Morrison's well-hit strike from the edge of the box squirmed underneath Joe Hart's poor attempt to save to send the visiting fans into raptures.
It took until the 26th minute for the hosts to provide the home fans with something to cheer, as Tom Cleverley went close following a delightful lay-off inside the box from Rooney.
Just three minutes later, they were level. Walcott darted in from the right to latch on to a well-weighted Cleverley through-ball, deceived Steven Whittaker, and squeezed the ball in left footed at the near post to restore parity.
The hosts were much improved after their equaliser, and they were only denied a second goal shortly before the break by an incorrect decision from the assistant referee.
Rooney was the unlucky recipient of the officials' attentions, with the striker wrongly flagged offside after collecting a Gerrard ball in the box on his chest and controlling to fire home.
Wilshere was the only man to depart at half-time, as the Arsenal midfielder made way for Frank Lampard with his troubling injury record clearly in mind, but there was little time for England to adjust to the tactical consequences of that switch before they found themselves behind for a second time.
Miller did brilliantly to hold the ball up on the edge of the box before turning a hapless Gary Cahill to smash home on his left foot, much to the dismay of the shell-shocked hosts.
But, unlike in the first half, it did not take long for England to muster a reply.
Just two minutes after Allan McGregor produced a brilliant save to keep out Gerrard's deflected free-kick, the England captain picked out Welbeck with another pin-point set-piece delivery which the Manchester United forward gratefully headed in.
A flurry of substitutions from both sides, which saw Lambert handed his debut, followed - and the striker soon had his dream moment.
The 31-year-old rose highest to meet a Baines corner from the left and directed the ball brilliantly home with his head to put the hosts ahead for the first time in the match in the 70th minute.
Chances were at a premium for the remainder of the game, but Lambert had one last opportunity to double his account in the dying moments.
However, the striker could only hit the post from close range following a cross from the right, though it is unlikely the miss will play on his mind much after a near-perfect debut.