McLaughlin struck on 32 minutes to ease any nerves the visitors had.
But they defended brilliantly for 90 minutes and Nathan Bishop's only real save came in the opening seconds from Northampton's first raid.
In truth there were few real chances at either end as Northampton's direct game was repelled superbly by the visitors.
The Stags side showed three changes from the first leg with George Maris ruled out with a knock and Matty Longstaff and Jamie Murphy dropped to the bench.
In came Kieran Wallace, Elliot Hewitt and Lucas Akins as Clough elected to push John-Joe O'Toole into an unexpected midfield role at his former club.
The Cobblers welcomed back first choice keeper Liam Roberts after he missed the first leg with suspension while Josh Eppiah also came into the starting XI.
Paul Lewis was named on the Cobblers' bench after recovering from a broken foot.
Amid a magnificent atmosphere, the home side almost grabbed the lead inside 50 seconds.
Hoskins crossed from the left after good work by Appere and Eppiah met it with a far post header that forced a superb save from Bishop to his right.
Both sides had corners cleared, then Stags then had to defend a couple of dangerous Pinnock long throws while a poor Perch clearance reached Sowerby, whose vicious shot cannoned up and over the top off Wallace.
Nigel Clough had said getting through the first 15 minutes would be crucial and Stags had safely negotiated that hurdle.
Instead the visitors roared into the lead on 32 minutes.
Hewitt was onside as he broke to the right by-line and crossed hard and low for the incoming McLaughlin to tuck away from close range.
Quinn would have been offside if he'd touched the ball so he intelligently left it for Hewitt to run on to.
McLaughlin then got a good block in on Eppiah's shot while Bishop crucially won a race to a through ball for the same player as the home side looked for a swift reply.
Wallace was hurt by a Sowerby blast he took full in the face but was able to continue.
On 40 minutes another long Pinnock throw caused a scramble in the six yard box in which Northampton were screaming for a penalty for a push with Hoskins eventually firing the loose ball over.
The earlier sunshine had by now long gone and heavy rain began to fall on Sixfields.
On 44 minutes Stags got into the home box again and both Akins and Hewitt had shots charged down as the visitors went in 3-1 to the good on aggregate and the tie theirs to lose.
A block tackle by Guthrie had Quinn in agony on the restart but the veteran was able to continue.
Two more tackles in the Stags box saw two more calls for a penalty with the home fans now incensed with the officials.
On 53 minutes O'Toole was booked for a foul, followed on 63 minutes by Wallace after he caught Eppiah late.
Ex-Stag Rose joined the action and dangerman Eppiah also had to be replaced as he continued to limp.
Hoskins saw a shot charged down and Sowerby an effort deflect wider as the home team desperately looked for a lifeline.
In a rare Stags raid on 74 minutes Quinn was too high with an overhead kick from 12 yards and soon after Oates had a snapshot blocked.
Wave after wave of home attacks were repelled superbly as Stags defended for their lives.
Lapslie took over from Quinn with eight minutes of the 90 to go and three minutes later Wallace was replaced by Clarke to give Stags fresh legs in midfield.
Bishop's handling continued to be magnificent as the balls continued to be pumped his way.
A frustrated Pinnock was booked for his challenge on McLaughlin on 87 minutes as the noise from the away fans increased with the finishing line approaching.
Five minutes were added and the home side forced two more corners, but Stags were in no mood to spoil their deserved clean sheet, which was the icing on the cake.
But, just after Horsfall was booked for dissent, the game was halted after a couple of minutes as three home fans inexplicably ran on the pitch, threw a smoke bomb in the direction of Stags players and one barged into Bowery before stewards wrestled them down and threw them out.
That couldn't take away from the final whistle celebrations as Stags basked in the glory of a forthcoming day out at Wembley.
NORTHAMPTON: Roberts, Sowerby, Guthrie, Horsfall, Hoskins, Pinnock, Koiki, McWilliams, Eppiah (Zimba 68), Mills (Rose 65), Appere. SUBS NOT USED: Harriman, Lewis, Kanu, Mexted, Dyche.
STAGS: Bishop, McLaughlin, Hewitt, Bowery, Hawkins, Perch, Quinn (Lapslie 82), Oates, Wallace (Clarke 85), Akins, O'Toole. SUBS NOT USED: Rawson, Murphy, Stech, Stirk, Longstaff.
REFEREE: Ben Toner.ATTENDANCE: 7,619 (1,463 away).