Leeds skipper Howson curled home a low shot in off the far post following a fine run in the 85th minute to clinch Leeds a fifth away win in the league this season and extend their unbeaten run to eight matches.
Burnley went in at the interval on Saturday with a two-goal cushion following goals from Brian Easton and Jay Rodriguez, but Max Gradel sparked the Leeds comeback with an emphatic finish seven minutes into the second half and Luciano Becchio hauled the visitors level with his sixth goal in five matches in the 66th minute.
Simon Grayson's side had won four times on their travels this season and laid siege on Burnley's goal in the closing stages before Howson produced a thrilling finale to lift his side up to fourth place in the table.
Burnley were unchanged from the side that beat Derby in their last game two weeks ago, while defenders Neill Collins and Paul Connolly returned for Leeds.
Gradel spurned two early chances for the visitors, who began impressively, first firing inches wide from the edge of the penalty area and then blazing over the crossbar when sent clean through on goal by Neil Kilkenny's defence-splitting pass.
Robert Snodgrass had a 25-yard shot blocked by Dean Marney and Burnley goalkeeper Lee Grant did well to parry another effort by Gradel before Chris Iwelumo forced Kasper Schmeichel into his first save in the 26th minute.
Schmeichel then kept out Andre Bikey's header following a corner, but Burnley then made Leeds pay for their earlier misses.
Bikey clipped a free-kick into the area and Easton pounced to lash home a left-footed shot into the top corner from six yards.
Collins headed Snodgrass's corner wide soon after, but the Clarets all of a sudden found themselves two goals up nine minutes before half-time.
Leeds centre-half Alex Bruce failed to deal with Clarke Carlisle's long punt forward and Rodriguez pounced to despatch a low shot beyond Schmeichel into the bottom corner.
The visitors were clearly rattled as Jack Cork and Dean Marney fired in long-range efforts, but hit back seven minutes after the restart.
Becchio's header found Gradel unmarked in the Burnley area and the Leeds winger applied a cool angled finish into the bottom corner from 12 yards.
Leeds seized back the initiative and after Iwelumo was wayward with a header the visitors struck a deserved equaliser following good work down the right between Connolly and Gradel, the former taking a return pass and crossing sweetly for Becchio to sweep the ball home from close range.
Snodgrass then hit the crossbar following a fine run and curling shot from outside the penalty area and after another marauding run, the Scotsman's cross deflected off Bikey's knee and was cleared off the goalline by Carlisle.
But Leeds were not to be denied and after Howson had carried the ball to the edge of the area, the Leeds skipper curled a brilliant low shot in off the far post to snatch all three points for his side.