Delph put in a fine performance as two goals from Christian Benteke gave Villa a much-needed victory in their fight against the drop.
And Sherwood, who has lifted spirits at Villa Park since his arrival as manager in February, was full of superlatives for the 25-year-old central midfielder.
He said: “I’m not going to go over the top here, but there isn’t a better midfield player in the country than Fabian Delph at the moment.
“He’s got everything, he breaks the game up, he’s got trickery, he bursts through with the ball. He has everything to his game, and he can score.
“I wouldn’t swap him for anyone in the mess we’re in. If you’re an Aston Villa fan, you’re loving him.
“He leaves nothing on the field. It’s not only about energy and desire, it’s about flair and imagination, he’s got the whole package. He’s a warrior, there isn’t a lot he can’t do.
“I see Roy Hodgson was up there, I think he would have been very impressed with the two midfield players, Cleverley as well.”
Sunderland’s 2-1 win over Southampton kept the pressure on Sherwood’s side but he believes they have momentum after climbing to 14th in the table.
He added: “I think there’s a bit of belief in there now. I think they’ve improved performance-wise since I came here and they’re looking like a Tim Sherwood side at the moment.
“What’s that? It wins! I think we’ve got pace, flair, goalscorers – we do score goals.”
Villa were nervous at times as Everton reduced the deficit twice, but Sherwood says the performance was dealt with under pressure, and that the clubs in the relegation fight may need over 40 points to survive.
“There’s a lot of pressure on us now, but the boys are coping with it really well and sticking to the game plan.
“We’re getting closer to the line but we need a few more wins. I think we need two more wins, maybe three.
“Everyone was saying it could be the lowest total ever, that’s rubbish, it could be the highest total ever.”