Swansea looked to have wrapped the game up by half-time after two goals in two minutes from Sinclair, the first from the penalty spot, were followed by another from Stephen Dobbie.
However, Noel Hunt gave Reading hope with a deflected near-post header from a corner shortly after the restart, and another header from Matt Mills just before the hour set up an exciting finale.
Jem Karacan was inches away from drawing the Royals level when his shot struck the post but Brian McDermott's side saw their hopes go up in smoke 10 minutes from time when Andy Griffin clumsily gave away a penalty which Sinclair gleefully converted.
In the process he became only the second player, after Clive Mendonca, to bag a play-off final treble at Wembley and ensured Swansea are the first non-English club to compete in the Premier League since its formation in 1992.
Victory ends a 28-year wait for top-flight football for Swansea and - aside from the estimated £90million windfall - completes an astonishing eight-year turnaround for the south Wales club after they narrowly avoided relegation from the Football League.
For manager Brendan Rodgers, it was victory against the club he served for a total of 14 years as player, youth coach, reserve coach and an unsuccessful six-month stint as boss in 2009.
His replacement 17 months ago, Brian McDermott, was able to call upon influential winger Jimmy Kebe after he passed a fitness test on a thigh injury.
Rodgers kept faith with the same line-up who saw off Nottingham Forest 3-1 in the second leg of their semi.
That meant defender Alan Tate and midfielder Leon Britton walked out for the club having been part of that dramatic final day survival in 2003.
And once the fireworks had gone off and the red carpet had been tucked away, it was the anticipated free-flowing, passing football which failed still to materialise in the opening exchanges.
Swans skipper Garry Monk survived a convincing appeal for handball in the penalty area, and no sooner had he got off the hook then Zurab Khizanishvili brought down Nathan Dyer at the other end.
It left Sinclair to send Adam Federici the wrong way from the spot and the Georgian centre-back lucky to avoid a second yellow card.
And just 60 seconds later, with 22 minutes on the clock, it was 2-0.
Khizanishvili was having an afternoon to forget and he was left standing by Dobbie on the right who squared the ball into the danger area and Federici's weak hand failed to stop it travelling to Sinclair who tapped home at the far post.
Swansea's lead was further strengthened five minutes before the break as Dyer used his pace down the right and his cross was only half cleared by Khizanishvili to the grateful Dobbie who fired home a third from the edge of the area.
Reading's 25-goal top scorer Shane Long then mis-kicked a glorious opportunity wide just before the break.
Matters went from bad to worse for the Royals at half-time as first-team coach Nigel Gibbs was sent to the stands and substitute Jay Tabb also dismissed for something said to referee Phil Dowd.
But the Berkshire outfit were given a glimmer of hope within four minutes of the restart as Hunt narrowly got in front of Joe Allen at the front post to head home Jobi McAnuff's corner, albeit via a deflection off Allen.
And the Wembley roof was soon raised yet again as Mills made it 3-2 in the 57th minute.
Swans once more failed to deal with a McAnuff corner from the left and the Reading skipper rose highest to head home from six yards.
Rodgers' side were rocking and Karacan saw his low 25-yard effort deflected against the foot of a post before Monk brilliantly denied Long on the rebound.
The clash remained firmly balanced as it approached the final quarter, but that all changed 10 minutes from time as Griffin brought down Fabio Borini in the area, leaving Sinclair to beat Federici for the second time from 12 yards.
And the strike was the cue for over 40,000 visiting Swansea supporters to party.