The former Tottenham man arrived from MLS outfit Toronto earlier this month, and marked his third appearance in all competitions with a simple close-range finish shortly after the half-hour mark.
Sunderland were already one ahead by that stage, as both Burnley centre-halves Jason Shackell and Michael Keane were drawn to the presence of Defoe inside the box, leaving Connor Wickham with an easy header from Anthony Reveillere's cross.
Burnley had mounted stirring comebacks in each of their last two away games, at Manchester City and Newcastle United, but there was to be no repeat performance at the Stadium of Light as Sean Dyche's side failed to create any clear-cut chances.
For Sunderland, meanwhile, it was a welcome victory - their first league win on home turf since early October lifting Poyet's men up to 14th in the table.
In a quiet opening to proceedings, Wickham's turn and finish was ruled out after the striker was adjudged to have fouled Keane in the build-up.
The visitors had the first notable chance in the 18th minute when Ashley Barnes headed David Jones' free-kick wide, shortly before Wickham put Sunderland ahead.
Jordi Gomez's clever ball picked out Patrick van Aanholt's run down the left and, with goalkeeper Tom Heaton committed, the defender's cut-back left Defoe with the simple task of tapping in from close range.
Burnley showed signs of encouragement at the start of the second half, as Barnes' header from Boyd's delivery was easily handled by Pantilimon before the striker's shot from the edge of the box was deflected wide.
