Curtis, making his first start since the end of October, scored twice in quick succession after youngster Aaron Taylor had headed the Shrimps into a 14th minute lead.
Chester had the first clear chance when central defender Paul Linwood forced a great double save from Barry Roche with a firm header on target from a Ryan Lowe free-kick.
But Morecambe soon took control as they took the lead with a well taken corner.
Michael Twiss, one of three former Chester players, produced a vicious in-swinger and Taylor nipped in front of his marker to direct a header past John Danby.
Chester rallied after the game and Kevin Ellison got the ball into the net with a glancing header only to see the offside flag raised.
But from there Morecambe dominated and should have scored a second after 27 minutes but Stewart Drummond missed the target from close range when he looked certain to slam home Neil Wainwright's cross.
Six minutes later, Morecambe did manage to double their advantage.
Wainwright again provided the ammunition with a storming run and cross down the left which Chester failed to clear and Curtis followed up to slam the ball home from 15 yards.
As half-time approached, Curtis hit his second to make it three with a stunning right-foot strike from the edge of the box from Taylor's neat knock down.
Chester came back strongly in the second half with a much better display.
Laurence Wilson gave them hopes of a comeback on 51 minutes when he scored a superb individual goal on 51 minutes after latching on to Wainwright's poor cross-field ball.
The visitors almost added a second a few moments later when Shrimps skipper Jim Bentley diverted a Ben Jones cross just wide of his own goal.
Roche made two decent saves from Lowe but it was the home side who came closest to scoring when Dave Artell headed a Garry Hunter corner inches over.