John Stones rose highest to head a corner in off the bar for his first goals of the season, doubling Everton's lead.
Adam Lallana vowed Liverpool will keep fighting for the top four despite their hopes fading.
The Reds' 0-0 draw at West Brom on Saturday left them playing catch up for the Champions League spots.
We'll dust ourselves down, go again, go to Hull (on Tuesday) and try to get three points to hopefully put as much pressure on the teams above us as possible.
I still feel that if we pick up maximum points from the remaining games, we'll be unlucky not to get into that fourth spot. It's still possible and while it's still possible, we'll keep giving our all.
We've just got to focus on ourselves. It'll be a difficult place to go - they're still fighting for their lives down at the bottom.
It will be a tough game, but we've got to go there and play our game and hopefully we'll get three points. You want to get back to winning ways as quickly as possible.
Everton broke down the right, and when United failed to clear the cross James McCarthy took advantage by bundling past Blind to fire home.
Striker Connor Wickham has every belief Sunderland can beat the drop despite their slide into the bottom three on Saturday.
While the Black Cats battled to a creditable 1-1 draw at Stoke, victories for Hull and Leicester meant those sides both leapfrogged the Wearsiders in the table, moving them from 16th to 18th.
"There are only five games left, but it is still a long way to go.
"And although it is going to be difficult, I think we have more than enough talent in the changing room to take on the teams we have got to play and get the points we need to stay safe."
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