FA Cup specialist Sam Vokes struck again to set the Clarets on their way to a fourth-round meeting with Bristol City as Burnley racked up another impressive Turf Moor win.
Vokes headed Sean Dyche’s men into a half-time lead to take his tally of FA Cup goals for the Clarets to four – all against Premier League opposition.
Andre Gray – whose hat-trick here in a 4-1 win on New Year's Eve blew Sunderland away in the Premier League – then came off the bench to guarantee a seventh victory in eight home games with his sixth goal of the season.
And the Clarets will have home advantage again against Championship opposition in the last 32 of the competition following City’s replay win at Fleetwood as Dyche's side keeps a remarkable season firing on two fronts.
The Burnley boss made seven changes from the side that had started last Saturday’s Premier League win over Southampton as he utilised the strength of the Clarets’ squad, with Vokes, Nick Pope, Tendayi Darikwa, James Tarkowski, Jon Flanagan, Joey Barton and Michael Kightly all coming in.
But the intensity of the performance didn’t drop in the opening stages of a third meeting between the two sides in the space of just 18 days.
Jeff Hendrick, whose influence is seemingly growing by the week, set the tone with an early strike parried by Vito Mannone before teeing up George Boyd for another effort which warmed the hands of the Sunderland keeper.
And Mannone had to be even more alert with 15 minutes gone to keep out a fierce drive from Boyd after the winger had been slipped in by Steven Defour.
The Clarets were pretty much in control throughout the first half against a Sunderland side which started with leading scorer Jermain Defoe on the bench in an effort to preserve his legs for their faltering league campaign.
And an increase in tempo again just before the break paid dividends.
Dyche’s side had passed the ball slickly all night from front to back and when Darikwa, again making the most of an opportunity to start at right-back, curled in another dangerous ball from the right flank Vokes did the damage.
The Wales international got ahead of Jason Denayer and with a perfect glancing header across Mannone into the far corner was able to celebrate his fifth goal of the season as he put Burnley 1-0 up.
Pope, making his home Burnley debut, had not been given a save to make and two minutes into the second half was able to watch a Seb Larsson effort curl narrowly wide as the Black Cats looked to respond.
That was confirmation, at least, that the Clarets needed a second goal to make life more comfortable and that almost came when Defour threaded through another pass for Vokes to get in a shot which was blocked by Papa Djilobodji.
Mannone then saved from Boyd and with just over an hour gone, Sunderland manager David Moyes sent on Defoe in a bid to sniff out a goal.
The Wearsiders enjoyed their best spell of the game as they tried to force an equaliser but Burnley’s back four, with Tarkowski enjoying an excellent first home start of the season alongside stand-in skipper Michael Keane, didn’t allow them a sight of goal.
And it was a substitution by Dyche that proved decisive in killing the tie off.
Gray had been on for less than 10 minutes when he dealt Sunderland another fatal wound, calmly slotting the ball past Mannone after Vokes had headed a Tarkowski ball into his path to stay one clear of Vokes at the top of the Clarets’ scoring charts.
In stoppage time Larsson almost pulled a goal back from a trademark free-kick but a flying save from Pope denied the Swedish international to provide another plus on a night of more positives for Dyche’s in-form side.
Burnley: Pope, Darikwa, Keane, Tarkowski, Flanagan, Kightly (Gray 75), Boyd (O’Neill 88), Barton, Defour, Hendrick, Vokes. Substitutes: Robinson, Mee, Lowton, Ward, Jackson.
Sunderland: Mannone, Jones, Van Aanholt, Denayer, Djilobodji, Larsson, Borini (Asoro 80), Manquillo, Love (Defoe 62), Honeyman, Januzaj. Substitutes: Domingues, O'Shea, Embleton, T Robson, E Robson.
Referee: M Jones
Att: 12,257 (1,377)