The Seagulls had the edge in a first half littered with free-kicks and they almost took the lead moments before the break.
A corner from Dean Cox was nodded goalwards by Adam El-Abd and Joel Lynch had a close-range header blocked on the line.
Brighton continued to take the game to Scunthorpe after the break.
The visitors had another escape when a header from Alex Revell was pushed out by keeper Joe Murphy and both Lynch and Guy Butters just failed to force in the rebound.
Scunthorpe's 25-goal marksman Billy Sharp had a frustrating afternoon. He had just a second-half booking to show for his efforts, but his partner Jermaine Beckford came to the rescue by giving them a flattering 65th minute lead with a superb solo effort.
The on-loan Leeds forward squeezed the ball through Butters' legs before slotting his sixth goal in ten games.
Brighton deservedly levelled seven minutes later when Revell headed on for Bas Savage to lift the ball over Murphy for his fourth goal in his last seven starts.
But an entertaining match ended in acrimony when Scunthorpe midfielder Matthew Sparrow had already been booked for a second-half foul when he was sent off in stoppage time for a bad tackle on substitute Joe Gatting.
Brighton defender El-Abd went down clutching his face moments later with a theatrical reaction which angered the Scunthorpe players.
Captain Andrew Crosby, a former Brighton player, refused to shake hands with El-Abd at the final whistle.