Amid overwhelming tension, Leeds winger Max Gradel was sent off in the 34th minute at Elland Road on Saturday for a skirmish with Rovers left-back Daniel Jones.
The incident sparked a fracas involving most of the players and Gradel had to be restrained by team-mate Micky Doyle after fighting with stand-in captain Beckford. Jones was booked for his part in the melee and referee Graham Salisbury lectured Simon Grayson for the Leeds manager's reaction to the furore.
Two minutes into the second half, Jones crossed from the left, Joe Kuffour turned the ball back into the goalmouth and Darryl Duffy turned to shoot Rovers ahead.
Howson replaced Shane Lowry in the 54th minute and the midfielder equalised five minutes later with a stunning 20-yard drive.
Then in the 63rd minute Bradley Johnson's cross was half cleared and Beckford lashed home the rebound.
Leeds held on in a nervous finale to spark a mass pitch invasion at full-time amid jubilant scenes as they ended three seasons in League One.