Again, they travelled to Turf Moor in impressive numbers.
Again, they left having had precious little to cheer.
Not until the 85th minute was the stand-in goalkeeper called into action.
A yellow card for Joey Barton drew some cheers, as did Jermain Defoe and Joel Asoro coming off the bench.
There was an enjoyable moment in the second half when Papy Djilobodji attempted, and pulled off, a scorpion kick when Burnley were bearing down on goal.
Otherwise it was another insipid display for the Sunderland faithful to endure.
Not until the 85th minute was the stand-in goalkeeper called into action, a tame header from George Honeyman straight into his arms.
He showed his shot-stopping abilities, but not until the dying embers of the game, when a Seb Larsson free-kick was arrowing towards the top corner.
Those were Sunderland’s only two shots on target in 90 minutes. It was a game they never threatened to take control of.
They started with a new shape, Billy Jones dropping in to form a three-man defence, Javier Manquillo and Patrick van Aanholt as wing-backs, Fabio Borini and Adnan Januzaj leading the line.
There were some encouraging signs, the extra man in midfield allowing a better and more energetic press; the extra body in defence making Sunderland less vulnerable to the high balls that destroyed them here on New Year’s Eve.
Burnley were still making the most of the running, George Boyd forcing two saves from Vito Mannone in the opening 20 minutes. Barton went close, too, when his effort from 25 yards was deflected towards the Italian’s bottom corner.
Sunderland looked relatively untroubled for the most of the half, but Burnley were even less ruffled.
The visitors had their fair share of ball, but never in particularly dangerous areas. There were only one or two moves of real note, built up on the left-hand side by Honeyman and van Aanholt. When the ball did get to the Burnley box, it was too easy to ease Borini and Januzaj away.
A Januzaj shot, blocked comfortably on the edge of the area, was the only opening they forged.
The hosts were hardly laying siege to the Sunderland goal but were getting joy in the spaces between the centre-halves and the wing-backs. It was there that the goal game, a crucial strike on half time. They broke down the right-hand side, Tendayi Darikwa crossing to the front post. Sam Vokes got their first and his glancing header was precise.
From that moment on, there was only ever one winner.
Sunderland’s attacking play worsened as the game went on, rather than improved. Not even the summoning of talisman Jermain Defoe made any difference.
The distribution from the back was poor, all too often straight at the Burnley defence or even straight out play. There was no presence up front, no one in midfield able to put their foot on it and change the tempo and pattern of the game.
Burnley may not have been free-flowing but they were always the more likely. Slowly but surely those long passes at the heart of the defence began to overwhelm Sunderland.
Vokes nearly settled it, Djilobodji getting back in just enough time, blocking as the Welshman pulled the trigger.
It was Andre Gray who finally put it to bed, ghosting through one-on-one as he did so regularly the last time Sunderland came to Turf Moor.
Moyes’ men exited the cup having barely thrown a punch.
If they stay up, it will matter not. Yet this was another performance to underline just how big a challange that is.