In a repeat of the first leg, the Chairboys dominated the opening stages and opened up a comfortable lead - only for the Pilgrims to leave them sweating later in the contest.
In the end, substitute Ryan Brunt's backheel was all they had to show for a much-improved second-half display but John Sheridan's men are condemned to another season at this level.
Wycombe boss Gareth Ainsworth, however, has the chance to complete a wonderful turnaround after saving his side from relegation from the Football League last year when they head to Wembley on May 23.
The home side went ahead on the night and doubled their aggregate lead after just eight minutes when Plymouth goalkeeper Luke McCormick failed to deal with Sam Saunders' corner.
Mawson's header across fell to captain Hayes, who hooked in from a couple of yards to replicate his opener at Home Park last Saturday.
The Chairboys almost added to their advantage soon after when McCormick redeemed himself by denying Aaron Holloway after he had been played in by Saunders.
The hosts were dominating the match, with Nico Yennaris heading just wide from Hogan Ephraim's cross.
McCormick then had to come to the Pilgrims' rescue again as he just about managed to tip Saunders' stabbed effort wide after Ephraim had picked him out.
But from the resulting corner, McCormick was at fault once more as Mawson beat him to Joe Jacobson's delivery at the near post and the ball nestled in the net.
It left Wycombe 5-2 up overall after what had been a one-sided first half as Plymouth failed to gain a foothold in the game before the break.
Their poor first-half display led to Sheridan gambling on a triple substitution with Jason Banton, Zak Ansah and Brunt all brought on.
Banton almost pulled a goal back inadvertently after an hour with a cross from the left that dipped over Wycombe goalkeeper Alex Lynch and came back off the bar.
The Pilgrims were now the ones piling on the pressure with Lynch being called into action by keeping out a low strike by Bobby Reid that bounced in front of him.
But the visitors were to pull a goal back when Ansah was played onside down the right and his cutback was flicked into the net by Brunt from just a few yards.
Ansah then had a chance to really set nerves jangling when he was found in space on the right - but Lynch pulled off a terrific save at his near post and when the final whistle went most of Adams Park was in jubliant mood.
Source : PA
Source: PA