The Scot says the playmaker is "coming up with the goods now" and also praised Shinji Kagawa after the Red Devils' emphatic win at St James' Park
Moyes smashed his club's transfer record during the January transfer window to bring Mata to Old Trafford from Chelsea.
The Spain international failed to find the net in his first nine appearances for the reigning champions but opened his account in last weekend's 4-1 home triumph over Aston Villa.
He doubled that tally with a sublime first half free-kick at St James' Park, added a second after the interval and rounded off matters with a cute backheel that allowed Adnan Januzaj to complete the scoring.
"I think Juan Mata's played really well and I think he's made us better," Moyes told reporters.
"He hasn't had the goals in the early games but I think he played fine. Recently he's started getting the goals and, more importantly, the assists as well.
"I think, over the last two seasons in the Premier League, Juan Mata was one of the best assist-makers.
"He's always got himself a good tally of goals and we needed that. He's coming up with the goods now."
The Scot also paid tribute to Shinji Kagawa who was handed a chance on Tyneside as Moyes made eight changes to the side that drew 1-1 with Bayern Munich in the Champions League on Tuesday night - casting an eye towards next week's return leg in Germany.
"Shinji played well," Moyes added. "Maybe a bit slow at the start but I thought as the game gathered momentum he was influential."