The Nigeria international had come off the substitute's bench after a long injury lay-off to score a late winner against West Brom at the Hawthorns a fortnight ago.
Anichebe followed that up today by cancelling out Darren Bent's opener for Villa just eight minutes after coming into the action.
Moyes said: "It was a great finish. Victor has had a terrible couple of years with injury.
"He can be a real handful and has got a good temperament.
"We need to get him on the pitch more often because we know what he is capable of doing."
Moyes admitted he feared the worst when Anichebe went down clutching his knee after falling awkwardly.
He said: "When I went down, I thought, 'Here we go again' after the bad luck Victor has had. But it was only a wobble in his knee.
"I think it was just a scare and he should be okay."
Donovan exuded class in his second loan spell at Everton from the Los Angeles Galaxy.
Moyes said: "I thought Landon was the best player on the pitch today.
"He has come over here from Galaxy, completed the full 90 minutes, and it is a testament to the professional he is."
Donovan's Galaxy team-mate, striker Robbie Keane, made a late appearance for Villa in what was his debut after joining the midlands club on loan.
Villa boss Alex McLeish said: "Robbie has not played for two or three weeks. He has come across the big pond (from America) and only trained for a few days.
"He is not going to be 100% after that short period and the other strikers have done well.
"But Robbie did well when he came on and I hope he can make an impact."
Villa ended a run of four successive home defeats and McLeish was content with the overall performance despite allowing Everton to salvage a share of the spoils.
He said: "With performances like that, the home wins will come. Aston Villa fans come here expecting to win and it was an improved showing on the performance against Swansea.
"We were concentrated and the work rate was much better."
Bent's seventh goal of the campaign put Villa in front early in the second period after he was teed up by the impressive Stephen Ireland.
But Anichebe timed his run perfectly to run onto a pass from Donovan for the equaliser.