With the Owls just one point above the relegation zone, it would have been reasonable to expect them to be nervous but they dominated from the outset against a Middlesbrough side that offered little.
Howard put Wednesday ahead in the ninth minute with his first goal for the club since joining on loan from Hartlepool in March before Lita, another loanee, added a second after half an hour against his former club.
A crowd of 31,375 witnessed the game although many of them would have approached it with some trepidation.
Dave Jones' side had appeared to be pulling clear of danger before a run of just two points from the previous four games plunged the Owls firmly back into trouble.
Defeat at Peterborough last week saw the South Yorkshire side start the game fifth from bottom and just one point above Barnsley who occupied the third relegation spot.
However, they knew their destiny was in their own hands: win or equal Peterborough and Barnsley's results and they would be safe.
Jermaine Johnson screwed an effort well wide after shrugging off the attention of two defenders and Seyi Olofinjana blazed over as Wednesday made their attacking intentions clear.
However, they were given a warning when Curtis Main escaped the defence and forced goalkeeper Chris Kirkland to smother at the Boro man's feet.
But Wednesday were in front in the ninth minute when Howard judged his run well and ran on to an incisive low ball before firing an unstoppable shot past Jason Steele.
And they doubled their lead after half an hour when Lewis Buxton's inswinging corner was glanced home by Lita in a packed six-yard box.
Wednesday's pace was troubling the visitors and they almost got a third moments later when only a desperate goal-line clearance prevented Howard from getting his second of the day.
Kirkland gathered a teasing cross in first-half injury-time but the break arrived with rapturous applause for Wednesday who had all but booked their Championship spot for next season.
Boro offered more after the break and Christian Burgess headed narrowly over from Grant Leadbitter's corner.
However, any fears were soon assuaged and the Wednesday fans soon got down to celebrating securing their Championship status - the final whistle prompting a pitch invasion.