Sharp signed from Southampton on Wednesday as Massimo Cellino responded to Leeds' opening-day defeat at Millwall and was immediately told by the former Cagliari owner to "hurry up and score some goals".
The 28-year-old left it until two minutes from time to obey the command but was in the right place at the right time to finish after Tomas Mejias failed to hold Michael Tonge's shot.
The late drama will have left a sour taste in Middlesbrough's mouth for it was they who did most of the running throughout and, to almost everyone in the ground, scored a legitimate opener through Albert Adomah which was ruled out.
It was Sharp who would have the final say, though, getting due reward for a grafting performance which nearly brought about a goal after only two minutes.
He ran on to a Souleymane Doukara flick and got into the box, only for Mejias to get out and smother at his feet. The ball then came free and fell to Nicky Ajose who, from 10 yards out, should have scored and not hit the recovering Daniel Ayala on the line.
That was as good as it got for Leeds in the early stages and they were soon being penned back by a Middlesbrough side who passed the ball round at a pace quicker than United could deal with and really should have been ahead 26 minutes in.
Liam Cooper failed to deal with a long throw into the box and turned to see Adomah overhead kick his half-clearance beyond Marco Silvestri. It looked a clean goal but referee Stuart Atwell had spotted an infringement and chalked it off.
Leeds managed to get hold of the ball on the half-hour and Tommaso Bianchi and Sam Byram had shots the caused little panic, but it was Middlesbrough who remained the more dangerous side and they would have led at the break were it not for Stephen Warnock.
Grant Leadbitter's pass put Adomah through in the six-yard box but, just as he was going to slot past Silvestri, Warnock appeared to shut him down with a brilliant block.
Jason Pearce was the next man to put his body on the line to keep Leeds level, diving in front of a Lee Tomlin effort as the hour approached, with Warnock then displaying his defensive nous once more to nip in and block of Kike as he ran through.
Leeds' best chance of getting something appeared to be under the suspect handling of Mejias who never looked comfortable under a cross and, with 11 minutes left he failed to reach a Luke Murphy centre but Sharp was unable to punish him from six yards.
But the former Doncaster man was on the spot as time ran down, showing the required poise to slot in after Mejias allowed Tonge's drive to slip away from him.