Becchio notched his ninth goal of the season with an audacious chip down the middle in the 42nd minute despite furious protests from Barnsley players, who felt Leeds skipper Lee Peltier had been fouled by Tykes defender Stephen Foster outside the box.
TV replays clearly showed this to be the case and a deflated Barnsley side, dominant for long periods in the first half, never properly recovered.
Leeds, outplayed before the break, were much stronger after the interval in a game of few goalscoring chances and climbed up to seventh place in the table after stretching their unbeaten league run to five matches.
Barnsley, last beaten by their Yorkshire rivals in an FA Cup clash in 2001, have taken only one point from three matches since rattling five past Birmingham live on television at the end of last month.
Manager Keith Hill will have been heartened by what he saw in the opening 20 minutes.
But aside from a long-range shot from David Perkins that whistled over the crossbar and an angled volley from midfielder Jacob Mellis, the Tykes had little to show for their early dominance on the ground where they triumphed 2-1 last season.
Barnsley continued to stretch their opponents, albeit without creating any clearcut chances, and Leeds fans had to wait until the 27th minute before their side's first effort on goal.
El-Hadji Diouf swung over a brilliant cross from the right and Becchio rose highest to power a header just off target.
Leeds began to wrestle back an equal share of possession as the first half progressed and midfielder Rudy Austin rifled an angled shot over the crossbar.
Barnsley striker Craig Davies saw his effort from the edge of the penalty area blocked by Leeds defender Tom Lees and Marlon Harewood pulled his low drive wide.
But Leeds stole into the lead three minutes before the break courtesy of referee Darren Deadman's controversial penalty decision.
Barnsley's players felt Foster's foul on Peltier had occurred outside the area, but Deadman pointed to the spot and Becchio out-foxed goalkeeper Ben Alnwick with a deft chip straight down the middle.
The Argentinian has scored in all five of Leeds' league games at Elland Road this season.
Barnsley defender Foster suffered a recurrence of his back injury and was replaced by Bobby Hassell at half-time, which did little to ease the visitors' sense of injustice.
Leeds midfielder Michael Tonge was forced off through injury soon after and replaced by David Norris, who made his first appearance in seven matches.
Chances remained at a premium as the second half unfolded. Austin's speculative 25-yard effort was comfortably gathered by Alnwick before opposite number Paddy Kenny denied the visitors an equaliser.
Harewood's close-range header from Mellis' 62nd-minute corner appeared goalbound, but Kenny saved superbly at full stretch to keep Leeds' noses in front.
Keith Hill sent on Chris Dagnall and Kelvin Etuhu for Harewood and Tomasz Cywka with 20 minutes left and former Barnsley striker Andy Gray replaced Becchio shortly later, but neither side mustered another chance and Leeds held on to their slender advantage.