The Lions skipper, whose recovery from a broken metatarsal meant he only started last season's 3-2 final defeat to Scunthorpe on the bench, smashed home from close range after Danny Schofield's corner had found its way through.
His 39th-minute goal was nothing less than the Lions deserved having posed the bigger threat throughout against a Town side who saw Charlie Austin slice wide a golden opportunity to level matters when clean through in the second half.
The victory - in front of 73,108 fans at Wembley - went some way to banishing the memory of five previous play-off defeats for Millwall, who were left celebrating a return to England's second tier following their relegation in 2006.
Lions boss Kenny Jackett stressed ahead of the encounter that "there is something in football, and life, in persistence" and his class of 2010 have proved just that.
And although it was despair for Swindon at the final whistle, their 12-month transformation from relegation contenders to promotion nearly-men under manager Danny Wilson deserves plenty of credit.
Millwall went into the clash without player of the year Alan Dunne, who had failed to recover from a foot injury, while Swindon were missing influential captain Gordon Greer due to suspension.
And it was the Lions who looked the livelier up front in the opening exchanges, 23-goal leading scorer Steve Morison coming closest to breaking the deadlock after 17 minutes when his delicate chip beat David Lucas but drifted inches over the crossbar.
Swindon finally settled somewhat midway through the half and an unmarked Lescinel Jean-Francois came within inches of connecting with Alan Sheehan's free-kick to the far post.
Kevin Amankwaah, a target of the Millwall boo-boys following his verbal spat with Neil Harris earlier in the season, inadvertently headed into his own net soon after only to see his error then ruled out for offside, much to the obvious joy of the 34,000-odd travelling Robins contingent.
But the half's defining moment came six minutes before the break when Robinson handed Millwall what proved to be the winner.
Swindon started on the front foot after the break although both sides were creating half-chances.
The second half was proving to be a much more open and even affair.
Town defender Jean-Francois came close to levelling when he saw his header well kept out by the diving David Forde, while Morison then fired straight at Lucas at the other end when he really should have done better.
But Swindon's best chance of the game arrived in the 72nd minute when Austin pounced on Robinson's mis-guided header to find himself clean through.
But the ball bounced up off the much-maligned Wembley turf just as the 20-year-old was about to shoot and his effort was uncharacteristically directed horribly wide.
Morison could have put the final beyond doubt in the last 15 minutes but he wasted a couple of great openings.
And it was left for Forde to deny Austin with a last-ditch save deep into the injury time to send Swindon's players to the ground and Millwall into the Championship.