Brighton had taken a 17th-minute lead thanks to debutant Matt Heath before Orient levelled on the stroke of half-time via Scott McGleish's penalty and then Thornton's goal condemned new Brighton boss Russell Slade to defeat in his first game.
In a tension-filled encounter, Orient had the first chance when Jason Demetriou picked up a short free-kick from Charlie Daniels and fired just wide from 20 yards.
Thornton also had an effort blocked before Brighton grabbed the lead on 17 minutes. Skipper Adam El-Abd sent in a ball that Orient keeper Jamie Jones failed to hold under pressure from Lloyd Owusu.
Heath stabbed his first effort against McGleish but followed up to scramble the ball over the line.
Brighton's Alhassan Bangura was lucky not to see red just before the break following an ugly challenge on Daniels but, moments later, referee Richard Beeby pointed to the spot when Heath turned from hero to villain by tugged Simon Church over.
McGleish smashed the spot-kick past Mikkel Andersen and Orient looked to build on their momentum at the start of the second half.
McGleish sent a header cannoning against the bar following a Daniels cross from the left and then, a minute later, Thornton had an effort ruled out for offside.
But Brighton hit back and Jones was forced to make a stunning save from El-Abd following Kevin McLeod's free-kick.
Craig Davies then shot just wide for the visitors and also sent an effort whizzing inches over the bar.
But in the closing minutes McGleish forced a good save from Andersen before Thornton latched on to Church's header, cut in from the left, and curled home a spectacular winner, his first goal of the season, two minutes from time.