Argentinian striker Becchio headed Leeds into a first-half lead after Michael Tonge had cancelled out Chris Atkinson's opener for Huddersfield.
Former Leeds midfielder Adam Clayton equalised for the home side from the penalty spot just before half-time, but David Norris edged the visitors ahead midway through the second period and Becchio ensured a thrilling derby win for his side with a header in the 86th minute.
It is Leeds' first win over Huddersfield in six attempts, while Town boss Simon Grayson, facing Leeds for the first time since being sacked at Elland Road in February, was left to reflect on just one win in his side's last six league matches.
The home side's made an early breakthrough when Danny Ward combined with Clayton on the edge of the area and the latter slipped the ball into the path of Atkinson, who ghosted in behind the Leeds defence to steer a neat finish into visiting goalkeeper Paddy Kenny's bottom right-hand corner.
But the visitors began to look dangerous on the counter-attack and struck twice in as many minutes shortly before half-time to turn the game on its head.
Ross McCormack first teed-up Tonge on the edge of the area in the 35th minute and the Leeds midfielder's low side-footed shot went underneath Huddersfield goalkeeper Alex Smithies.
Two minutes later, McCormack was the provider again, setting up Becchio in a similar position after another swift break by the visitors and the Argentinian slammed home his 13th goal of the season into the top corner.
But Becchio then turned villain for the visitors, penalised for pulling Huddersfield skipper Peter Clarke in the area following Ward's free-kick and Clayton stepped forward to steer the subsequent spot kick into the bottom corner.
Leeds were rewarded for another concerted spell of pressure with a third goal in the 70th minute.
Substitute Ryan Hall beat his man on the edge of the box and squared the ball for Norris to bury a left-footed finish inside Smithies' left-hand post from 12 yards.
The visitors then made the game safe in the 86th minute when Becchio powered home Hall's left-wing cross to make it a happy return to the John Smith's Stadium for Leeds' former Huddersfield boss Warnock.