Bolton striker Eaves signed on loan for a second spell at New Meadow on Thursday after scoring six goals in 10 games for the club at the end of last season.
"Tom's goal was vital to us and his partnership up front with Gozie (Ugwu) I thought looked very strong," said Turner.
"The one thing we know about Tom is that he can score goals, some people have that knack.
"It feels great, the dressing room's buzzing and I felt we deserved it, we've felt we deserved a few better results from other performances away as well.
"We opened the game up very well with our passing, it's been a terrific performance against a difficult side.
"You're always a bit concerned when you're ahead and they kept putting bigger players on.
"They're going to get loads of balls into our box and you can't stop all the service but I thought we dealt with it very well.
"It's a long, long time before we play again and it's just as well we got those three points.
"Our away support are terrific, they've stuck with the side through a lot of thin times and we hope that's just the start for them."
Zoko tapped in after 24 minutes, but Reach lifted over the on-rushing Chris Day 10 minutes later to equalise for the Shrews.
Eaves then nodded in Paul Parry's cross seven minutes before the break and Jacobson sealed the win when he headed home after 51 minutes.
- Sports & Recreation
- Joe Jacobson
- Adam Reach