Forest were the better team in the first period but the dismissal of Chris Cohen for a lunging tackle on George McCartney swung the game in Leeds' favour.
And the Whites took full advantage after the interval with Howson (51), Becchio (58) and Gradel (73 & 86) helping Simon Grayson's side climb up to fourth ahead of the 3pm kick-offs and leave counterpart Billy Davies without a win in his side's last eight matches.
A forgettable opening 20 minutes was punctuated by a flowing Forest move that spawned the game's first clear-cut chance, with left-back Joel Lynch crossing to the far post where a lunging Marcus Tudgay failed to keep his shot on target.
Leeds responded through Robert Snodgrass, the Scotland international firing straight at Forest goalkeeper Lee Camp after neat footwork allowed him to cut inside on the edge of the area, but both sides lacked the composure required to take control.
Forest substitute McCleary replaced the injured Paul Anderson in the 30th minute and then a tedious struggle exploded into action five minutes later.
Radoslaw Majewski wriggled clear of several challenges on the left side of the area and with Kasper Schmeichel stranded Tudgay somehow failed to find the net, his shot blocked by Leigh Bromby on the goal line.
Then Cohen lost his head, lunging in at Leeds left-back McCartney with both feet up in front of a furious Leeds dugout.
Cohen pleaded his innocence, but following the subsequent furore referee Halsey showed the Forest right-back a straight red card.
Forest's 10 men held out comfortably until half-time as Leeds laboured to work up a head of steam.
Gradel lifted his shot over the crossbar after McCartney's storming run shortly after the restart.
But Leeds broke the deadlock in the 51st minute. Snodgrass clipped a fine pass with the outside of his boot into Eric Lichaj's path down the right and the American's cross was turned home by Howson from close range.
Camp saved smartly with his feet to deny Bradley Johnson at the far post following Barry Bannan's free-kick, but was unable to keep out Leeds' second in the 57th minute.
Bromby headed Bannan's corner down and against the post and Becchio reacted quickest six yards out to head home the rebound.
Gradel wasted three golden chances to extend Leeds' advantage when sent clear into the area and then Forest hit back.
McCleary turned inside Bannan on the right edge of the area and curled a stunning 20-yard shot into Schmeichel's top right-hand corner.
Leeds were then indebted to Schmeichel who saved brilliantly to deny Wes Morgan's effort following Majewski's corner, before easing their nerves with a decisive third goal in the 74th minute when Gradel lashed home a bouncing ball into the bottom corner from the edge of the penalty area.
Leeds substitute Jake Livermore, on his debut, forced Camp into another fine save and the Forest goalkeeper followed up in superb fashion to deny Becchio, but Gradel pounced on the second rebound to put the result beyond doubt.