Leadbitter broke the tedium with a sweet 58th-minute free-kick, although Boro played with a man light for the final half-hour with Daniel Ayala red-carded for hauling down Fernando Forestieri.
But it was Boro who added a killer second in a moment that young goalkeeper Joe Wildsmith will want to forget with his clearance being charged down by Negredo on 67 minutes. De Roon added a stoppage-time third for the hosts.
A lifeless, sterile first half was almost totally devoid of chances and incident, with nothing happening aside from a couple of half-chances for the hosts.
The recalled Ayala, making his first appearance since October 22, fired over on 27 minutes with Wildsmith stranded outside of goal following a free-kick, and seven minutes later Adama Traore cut inside and saw his low shot blocked by Barry Bannan.
Despite struggling to create anything, Wednesday – who had made six changes to their starting line-up – were comfortable enough in possession and will have been happy enough at the interval, certainly with the scoreline after restricting Boro to next to nothing.
The action did not get better on the restart, only for the tie to finally burst into life just before the hour-mark.
First, Leadbitter fired Boro ahead with a quality free-kick after Bannan was penalised for a foul on de Roon, but within a minute the hosts were down to 10 men with Ayala shown a straight red card after chopping down Forestieri as he was about to burst into the box.
It looked like being a long final half-hour for Boro, but a bit of relief was afforded them on 67 minutes in a horrific moment for young goalkeeper Wildsmith.
He dallied too long with a routine clearance and, when he did finally attempt to clear his lines, the ball was charged down by Negredo into the empty net for a comical second for Boro.
The strike floored the Owls, with an offside flag denying Cristhian Stuani after he diverted in Negredo’s cross-shot.
It took until 83 minutes for Wednesday’s first effort on target with David Jones’s header easily saved by the under-employed Brad Guzan, who also grasped a late shot from Forestieri.
De Roon added a late third with an emphatic finish after Wildsmith blocked Stuani’s initial shot.
Middlesbrough: Guzan; Chambers, Ayala, Bernardo, Friend; Clayton (Downing 62); Stuani, Leadbitter; De Roon, Traore (Fabio 62); Negredo. Unused substitutes: Dimi, Gibson, Forshaw, Rhodes, Gestede.
Sheffield Wednesday: Wildsmith; Palmer (Joao 72), Lees, Loovens, Pudil; Wallace (McManaman 45), Bannan, Jones, Reach; Forestieri, Fletcher (Nuhiu 71). Unused substitutes: Dawson, Semedo, Hunt, Sasso.
Referee: D Coote (West Yorkshire).
Attendance: 23,661 (3,283 Sheffield Wednesday supporters).