The result lifted Shrewsbury seven points clear of the relegation zone with Crawley having no answer to the finishing prowess of Eaves, 21, who has scored six goals in eight games since arriving on loan from Bolton.
Eaves cracked home an unstoppable 25-yard drive to break the deadlock three minutes into the second half.
He then ran from the halfway line before lifting the ball over goalkeeper Paul Jones and, after skipper Matt Richards blasted a penalty over the bar, Eaves completed his treble five minutes from time with another powerful shot from distance.
"Tom has produced an unbelievable hat-trick," said Turner. "They were terrific goals and he's done what he's in the side for.
"I think his hat-trick is as good as you get. He might have had a bit of luck with the second one where he had a couple of ricochets but his determination took him through a couple of tackles and he had the composure to finish it off.
"The other two were tremendous strikes - he does really get hold of the ball and strike the ball well. He's got six goals in eight games which is an incredible record for us."
Turner felt it was a day when the vital breaks went the way of his side. But he still feels there is work to be done and that Shrewsbury need a couple more points to guarantee their place in League One for next season.
"I would like to say it was a terrific performance and the scoreline was a reflection of our dominance but I don't think I can," he added.
"We've probably had the luck that we've been missing over a period of time. Crawley looked a good side and caused us problems with their movement."