The former Western Samoa international’s header cancelled out Newcastle’s controversial opener to lanky striker Shola Ameobi and sent his side to fourth.
After the match Moyes was full of praise for the 26 year old.
“You just need to look at Tim’s goals this season, he’s got four now and that’s a great return. He’s one of the best at getting in the box,” he said.
“We can play him in the middle of the park, or in between the strikers and midfield, or we can play him up top. We’re playing him slightly further forward than a central midfield player.
“He’s as good as anyone in the business at getting into the box and scoring goals. He’s robust and wholehearted and does a good job for us.”
Cahill’s effort from a Mikel Arteta cross obviously pleased Moyes, but he was still left fuming at Ameobi’s opener.
“I’ve not seen an offside like it. I really am trying not to mention referees and linesmen this season because I make mistakes and so do my players.
“We push up for offside, Ameobi’s the last man, the ball goes directly to him and he scores so you can’t even say there was a mix up. What do I do? Do I just stand back and say that’s fine? I’m passionate about winning for Everton and we got a bad decision.
“I don’t want my players to mob officials. The referee had a good game but I didn’t think both the assistants did.”
Both sides ended the ill tempered match with 10 men, with defender Tony Hibbert and Titus Bramble earning early showers with two bookable offences.
“Both sendings-off were correct,” said Newcastle manager Glenn Roeder.
“Both were poor decisions to tackle, and both mistimed. Titus wouldn’t have made that challenge in the first minute but he’s gone right through the back of the lad and it’s very hard to make a case for him.”
Bramble will now receive an automatic one match suspension and join fellow defender Celestine Babayaro on the sidelines, leaving the Tyneside club short in the defensive stocks.
They may also have a problem up front with goalscorer Amoebi leaving the field with an ankle injury.
“It’s too early to say on Shola,” the Newcastle manager said.
“He turned to run, put his right foot down and felt something quite sharp in his ankle go. Until we have it scanned on Monday we won’t know, we hope it’s not too serious.”