Dario Gradi's side continued their fine run of form and leapfrog the Devon visitors to move into 12th spot in the Championship.
The Cheshire side had not been beaten at home in five games and there was little danger that they would lose this one once Clayton Ince had palmed David Friio's third minute header from close range over the bar.
Plymouth boss Bobby Williamson left out unsettled striker Steve Crawford from the starting line-up and deployed Micky Evans as a lone front man.
And while the visitors enjoyed a lot of possession they were never anywhere near as threatening as Crewe were when they got to the box.
Steve Jones wasted a tenth minute opportunity when he shot straight at Romain Larrieu after David Vaughan's pass had freed him on the right of the box.
Vaughan headed wide when well-placed and Lunt should have scored himself instead of squaring for Steve Jones to apply the finish. Argyle centre-half Graham Coughlin saved the day with a timely interception.
Ince did likewise at the other end as he tipped over David Norris' 25-yard screamer.
But Crewe took the lead three minutes before the break when Ashton was fouled by Peter Gilbert. From just outside the area Lunt unleashed a right-foot free-kick which flew from one side of the wall into the bottom corner of the net.
Plymouth had the better of the early part of the second half, but Ashton extended Crewe's lead in the 57th minute after Steve Jones' pacy run was halted in its tracks.
There were appeals for a penalty as Jones tumbled under a challenge from Mathias Doumbe but Ashton seized the loose ball and squeezed it across the keeper into the far corner.
And the 21-year old striker, who was being watched by Birmingham City manager Steve Bruce among others, completed the scoring ten minutes time when he chased on to Lunt's through pass.
Doumbe tried to intervene but the ball trickled past Larrieu into the net with Ashton claiming his second.
After the match Crewe boss Dario Gradi said: "That was much better than we have been doing although we had a second-half wobble but we got it right and got going again.
"Dean was terrific. He is getting more consistent every week and is doing good things and always looking dangerous."
Pilgrims manager Williamson said: "This was a bit of a travesty. We weren't three goals worse than Crewe.
"Our fans paid their money and they will be disappointed with that but I think they will still come and support the boys at Derby next week.
"I am not the sort of manager that gets too high when things are going great so I won't get too low when they are not going so well."