Fulham boss Lawrie Sanchez left the north-east once again bemoaning his side’s inability to hang on to a lead.
For much of the first half and a chunk of the second, the Londoners looked well on top as Sunderland struggled for fluency.
But real chances were at a premium for the Cottagers, and it was a strangely familiar story for them in the end.
They failed to hold on to the lead given to them by Simon Davies’s excellent first-half free kick.
And they might even have lost the match in injury time if it hadn’t been for goalkeeper Antti Niemi’s save from Anthony Stokes.
Sanchez said: “I think only one team should have won the game.
“Only one team looked like it was going to win the game and to be undone with five minutes to go is disappointing.
“But for Antti’s save at the end we could have gone home with nothing, which would have been a gross injustice.
“That’s football. If you don’t take your chances when you’re ahead, it is open for the other team – especially if it’s the home team – to chuck everything at you and hope that something ricochets in.
“They put enough balls into the box for the big man (Kenwyne Jones) and his goal was the only one he got on the end of.
“We played Wigan and had an identical situation. We completely dominated them and then gave a penalty away with 10 minutes to go.
“It is getting to be a bit of a scenario that we have to sort out.”
Saturday’s draw left Fulham a place above Sunderland, at 15th in the Premier League on nine points, due to a better goal difference.
Both clubs are only two points above the drop zone and Fulham have won only once.
“We do an awful lot of things well,” Sanchez said of his men. “We’re a decent side.
“It’s just performing for 90 minutes and getting away with all of the points that we’re finding difficult. It depresses me.
“I see some results in the Premier League with teams conceding six and seven goals, even three or four. We had one bad afternoon against Portsmouth and were beaten 2-0. That was our worst result.
“We’ve been in every other game – even against top teams like Arsenal.
“We can compete, but we can’t gather three points from one game – we have to do it in three games, which does make it rather difficult.
“If we play like that in 90 per cent of our games, barring the last five minutes, we will be okay.”