Boro's Gareth Southgate brought in Brad Jones in goal in place of Ross Turnbull, while Lee Cattermole came in to bolster the midfield.
The visitors made a perfect start as record signing Afonso Alves played the ball through to strike partner Tuncay in the fourth minute and he placed a firm, low shot beyond the advancing Craig Gordon.
However, the lead lasted a matter of two minutes before Sunderland hit back. Danny Collins floated in a cross from the left flank and Danny Higginbotham arrived right on cue to power a header past Jones.
Twelve minutes in Chopra came close to giving the home side the lead with a shot as Jones hesitated.
Tuncay then headed narrowly wide of the target as both sides continued to carve out chances as the half-hour mark approached.
On the stroke of half-time Sunderland took a 2-1 lead when Chopra turned his marker, David Wheater, after collecting a Liam Miller pass and placed a left-foot shot past Jones to send the home fans wild.
The recalled Chopra continued to look sharp straight after the restart, threatening with a couple of efforts as the home side went in search of a killer third goal.
Just before the hour Southgate brought on Fabio Rochemback in place of Cattermole, who had struggled to make an impact in the midfield engine room.
Soon after home boss Keane brought on Grant Leadbitter for Carlos Edwards, who was clearly some way short of full fitness.
Chopra spurned another opportunity just before Emanuel Pogatetz clashed heads with Kenwyne Jones and needed treatment for a nasty-looking nose injury.
Boro were back on level terms with 17 minutes left to play as former Black Cats midfielder Julio Arca fed Alves and the Brazilian coolly beat Gordon with a right-foot shot from 12 yards out.
However, with time running out there was a twist in the tale as Leadbitter's corner from the left was turned into his own net by the unfortunate Pogatetz.
That left Sunderland celebrating Premier League safety, while Boro must endure a nervy last couple of weeks of the season.