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.
The goals earned Sunderland just their second win in 13 league outings, and sealed a potentially crucial three points against a side likely to be embroiled in a relegation scrap come the end of the season.
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.
Reveillere got in behind the Burnley backline on the right and delivered a perfect cross for Wickham who was left all alone to nod home from six yards.
George Boyd had a chance to equalise just before the half-hour mark, but he was off-balance as he shot and the effort lacked the requisite power to defeat Costel Pantilimon.
With 34 minutes gone, Sunderland doubled their lead thanks to Defoe.
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.
Danny Ings - the subject of speculation about a move to Liverpool this week - was largely ineffective and was replaced by Lukas Jutkiewicz on the hour mark, with Ross Wallace also coming on in place of Boyd.
The changes failed to have the desired effect, however, as Sunderland were able to comfortably see out victory and leave their opponents remaining a point and a place above the drop zone.
