The Argentinian striker was rested for Saturday's 2-0 loss at Hull in which Leeds failed to register a shot on target, but he showed his team-mates how it was done as he scored his 18th goal of the season from the penalty spot after 65 minutes.
Bolton could stake a claim for an undeserved defeat - they had the best of a torrid first half during which they hit a post.
Darren Pratley robbed Alan Tate of possession in the centre circle and he and Kevin Davies worked the ball to a clean-through Chris Eagles, but his shot clipped the post and went behind.
Eagles brought about the best moment of an awful half when he forced Paddy Kenny to tip his 35-yard shot around the post.
Becchio's goal after Tyrone Mears' clumsy foul not only earned Neil Warnock's men a fifth straight home win for the first time since 2009, it also booked him a spot in Leeds' all-time top-10 leading goalscorers on 76.
It means United remain in touching distance of the play-offs, but Warnock will surely still need new owners GFH Capital to give him the backing he has asked for if they are to mount a genuine push, as winning without playing well can only last for so long.