Departing crowd favourite El-Hadji Diouf netted a superb 42nd-minute opener and Black Cats substitute Daryl Murphy headed into his own net in the closing stages to seal the result.
"We knew the scores as they were coming in but didn't make a difference to what we were trying to actually achieve," said Megson.
"The consequence of getting the three points very much made the difference.
"The players knew they needed to perform today because we're going to Chelsea next week.
"It's four years since they lost at home isn't it?
"So we knew when we kicked off that if we could get a result it would put an awful amount of onus on the other teams, but we still had to get the actual win.
"Now we are three points above the relegation zone and in a great position to stay up."
Sunderland, for their part, arrived in Lancashire safe from relegation - and it showed.
But furious manager Roy Keane admitted there was no justification for such a meek surrender.
The Black Cats were second best throughout and their performance prompted Keane to point an accusing finger at his players.
Keane said: "We gave away bad goals again, which I've been saying for 38, 40 weeks now.
"We've lost 22 games now this season and people keep telling me we've had a good season - but I'm lucky to be in a job.
"You learn a hell of a lot about your players all the time and today has just confirmed what I'm thinking anyway.
"I made three substitutions today but I could have made 10. I think they should change the rules so I can make 10 substitutions."