Leeds goalkeeper David Lucas made his first league start since February after a solid display in the midweek Carling Cup win over Crystal Palace. Rovers not surprisingly kept the side that thrashed Hereford 6-1 last week but they were behind after only five minutes.
Neil Kilkenny exchanged passes with Fabian Delph before finding Beckford, whose shot from inside the penalty box deflected past keeper Steve Phillips off defender Steve Elliott's hand.
Elliott was credited with an own goal in Leeds' 1-0 win over Rovers last season and although Beckford tried to claim the credit this time, Elliott's name will again go down in the records.
Ironically, just two minutes before the goal, Rovers striker Rickie Lambert also had a shot deflected but he was unlucky to see the ball fly outside a post. And when Jeff Hughes tried his luck with a left-foot volley on 17 minutes his effort also zipped just wide.
However the equaliser arrived in he 32nd minute when Paul Huntington made a fine blocking tackle just outside the penalty box. The ball rebounded to Lambert and with the defence out of position, he made ground before shooting past the stranded Lucas for his fifth goal of the season.
Five minutes later Rovers were ahead, Darryl Duffy exploiting generous space as he met Chris Lines' free-kick and produced an accurate shot from ten yards.
Leeds attacked for most of the second half and equalised on 77 minutes when substitute Enoch Showunmi threaded the ball through for Beckford to net with a cool chip.