The Black Cats took a major step towards survival on Saturday afternoon as they beat Chelsea 3-2.
That win at the Stadium of Light saw the move out of the relegation zone and push rivals Newcastle United back into the bottom three.
They are now a point ahead of Rafa Benitez’s side and have a crucial game in hand in midweek.
That is against Everton, who were battered by Leicester City on Saturday, and Savage has predicted Sunderland will get the victory they need.
"What a fantastic win against Chelsea - Jermain Defoe just scores you goals,” he told BBC Radio 5 Live 606.
“But Newcastle can't even beat Villa. Does that now mean they're down? Watching Everton against Leicester, they were woeful. I think Sunderland will beat Everton and Newcastle are relegated.”
Sunderland will certainly be confident of getting the win they need in midweek given how Everton played at the Kingpower.
The Blues were blown away by the champions in that game, and ultimately were fortuitous to leave with just a 3-1 loss to their name.
They are a side that is bereft of confidence or motivation at present, as the pressure continues to rise following another disappointing campaign.
Sunderland will be the exact opposite after the huge win over Chelsea and survival certainly seems certain at this point.