A Stephen Caldwell header midway through the second half was enough to consolidate Sunderland's play-off spot and condemn Leicester City manager Craig Levein to his first defeat since he took over at the Walkers Stadium.
Sunderland substitute Chris Brown might have added a second when he struck the crossbar, while City's David Connolly had a late effort cleared off the line.
Keith Gillespie almost caught Thomas Myhre napping within seconds of the start with a 12-yard drive from a tight angle.
On 18 minutes, Gary Breen gave the ball away to Connolly and his first-time shot from 20 yards flew narrowly wide.
Darren Carter squandered Sunderland's best chance for the first half on 34 minutes when he ran on to a pass from Marcus Stewart and shot over from 12 yards with only the keeper to beat.
Sunderland went close again a minute after the restart when a shot by Darren Carter was deflected by Danny Tiatto into the path of Elliott, whose close-range drove was blocked by Kevin Pressman.
Carl Robinson found himself with only the goalkeeper to beat but he was denied a shooting opportunity by a great tackle from Jordan Stewart.
Pressman had to be at his best to tip a 15-yard volley from Brown over the bar, but from the resultant corner the visitors took a 69th minute lead.
Dean Whitehead swung the corner over and Caldwell got in front of Pressman to head home from three yards.
After Elliott had shot into the sidenetting from a good position, Sunderland went closer when Brown struck the crossbar from 25 yards after a determined run had taken him beyond three defenders.
Leicester almost levelled three minutes from the end when James Scowcroft nodded on to Connolly whose angled shot was parried by Myhre.
Connolly seized on the loose ball and chipped over the stranded keeper, but Whitehead had got back to head the ball off the line.