Barnsley had the better of the play in the opening stages, with Jacob Mellis going close on two occasions for the visitors.
El-Hadji Diouf proved to be a threat to the Barnsley defence throughout and his dangerous cross should have been converted by Becchio but the striker sent his header over the crossbar.
The hosts were handed the opportunity to break the deadlock before the break when Lee Peltier was brought down by Stephen Foster and despite the Barnsley defender's insistence that the challenge took place on the edge of the area, the referee pointed to the penalty spot.
Becchio stepped up from 12 yards and chipped the ball into the back of the net for his second successful penalty kick in a week.
Despite the setback before the break, Barnsley responded well in the second half and Marlon Harewood was denied an equaliser by a superb Paddy Kenny save before the hour mark.
The visitors struggled to create any chances late on and Leeds were able to control possession to secure a win against their rivals.