The Argentinian striker kept his composure after the ball had rebounded to him off Boro goalkeeper Jason Steele in the 91st minute to smash the ball home from 15 yards and extend Leeds' unbeaten run to 12 matches.
It was rough justice on the visitors, who looked to be heading for back-to-back victories after David Wheater's towering header had given them a first-half lead they rarely looked like surrendering.
Leeds announced the permanent signing of on-loan centre-half Andy O'Brien from Bolton before kick-off, but appeared to run out of steam against Tony Mowbray's well-organised outfit.
Andrew Hughes, at left-back, and Becchio returned for Leeds and Middlesbrough also made two changes, with Scott McDonald up front and Nicky Bailey recalled to midfield.
Leeds winger Robert Snodgrass volleyed over the bar from 20 yards in the ninth minute following Becchio's knockdown, the only effort on goal in the opening 15 minutes.
But after Leroy Lita's angled drive was deflected for a corner in the 20th minute, Julio Arca curled the ball over and Wheater rose above the home defence at the near post to head beyond Kasper Schmeichel.
Leeds gave the ball away regularly and were almost punished again in the 35th minute when Arca was left free to run on and fire a low shot from outside the area just wide of Schmeichel's left-hand post.
Arca then curled a free-kick over the bar after Hughes' foul on Marvin Emnes, for which the Leeds defender was booked, as the home side struggled to make headway.
Leeds' frustrations continued after the interval and were manifested in a 52nd-minute booking for skipper Jonny Howson for a trip on McDonald.
Leeds manager Simon Grayson made a double substitution in the 56th minute, sending on Lloyd Sam and Neil Kilkenny for Max Gradel and Hughes.
Ross McCormack flashed a curling free-kick just wide and Sam dragged a shot the wrong side of the post soon after as Leeds stepped up their bid to get back in the game.
But Boro threatened again when left-back Joe Bennett displayed dazzling skill to weave his way into the box before lifting a shot over the bar.
Grayson threw on Sanchez Watt for Snodgrass in a last-ditch effort to grab a draw and McCormack looped a ball off target in the closing stages before Boro goalkeeper Jason Steele saved smartly from Watt's angled shot in the 89th minute.
But with the clock ticking down Kilkenny played a hopeful ball into the area and after McCormack's header the ball rebounded to Becchio, who lashed the ball home on the volley to rescue an unlikely point for the home side.