The Blues' striker demonstrated three clinical finishes to help extend City's unbeaten run to three games.
Chester condemned the Mariners to another miserable scoreline which flattered the Blues.
Grimsby enjoyed long spells of possession and created countless chances, but were thwarted by City keeper John Danby's shot-stopping skills and, unlike Chester, they failed to convert their chances.
Blues boss Simon Davies made two changes from the side that were held to a 1-1 home draw the previous week by Bury.
Defender Laurence Wilson was sidelined with a calf injury, and striker Paul Taylor was struggling with food poisoning, and they were replaced in the starting line-up by Shaun Kelly and Richie Partridge.
The Blues started the contest on a positive note, breaking the deadlock after just three minutes when Ryan Lowe laid a pass into Kevin Ellison's path who raced clear of his marker before slotting a low shot into the bottom left corner of the net.
Chester looked full of confidence during the early exchanges and could have doubled their advantage in the seventh minute when Richie Partridge latched onto a Damien Mozika pass and directed his effort wide of the left post.
Grimsby hit back in the eighth minute when Javan Vidal sprinted along the right flank and forced City keeper John Danby into a catch.
Mozika was pulling all the strings for the Blues in the middle of the park and set-up Ryan Lowe in the 13th minute whose 20-yard shot was held by home keeper, Phil Barnes.
Grimsby, who hadn't won a league game since March, continued their search for an equaliser in the 14th minute when Nick Hegarty's left wing centre just eluded ex-Wrexham striker Chris Llewellyn.
And the Welshman saw his glancing header in the 16th minute from Danny Boshell's free kick fly over the bar.
Lowe was presented with a gilt-edged scoring opportunity in the 26th minute from Mark Hughes, but his angled effort from the left edge of the area rolled inches wide of the far post.
Grimsby countered two minutes later when Danby completely missed Vidal's right wing cross and Llewellyn reacted sluggishly before the danger was cleared.
And the home club worked hard to get themselves back on level terms before the break.
Boshell's 31st minute free kick fell for substitute Simon Heslop who volleyed wide from 10 yards, and Tom Newey forced Danby into a tip-over save after a one-two with Nathan Jarman.
Danby came to City's rescue in the 36th minute when he made a superb save to deny Peter Till's volley following a cushioned header from Newey.
And James Vaughan helped retain Chester's one-goal advantage a minute before the break when he headed Matthew Heywood's free kick off the line.
Llewellyn was offered the last chance of the half before he was substituted at the break, but he headed over the bar from Vidal's right wing cross.
Grimsby enjoyed a bright opening to the second half, helped by Llewellyn's replacement Danny North, who swept home the equaliser from close range in the 49th minute after City failed to clear Boshell's right wing corner.
Danby continued to illustrate his shot-stopping skills when he pulled off a superb reflex save to deny Jarman off Newey's cross.
Grimsby came close to taking the lead two minutes later when Boshell's shot off North's cross was pushed onto the bar by Danby.
Boshell then squandered another superb scoring chance in the 74th minute when he screwed an effort wide of the left post after an accurate delivery from Vidal.
The Mariners were punished for their failure to finish in the final third when Chester doubled their account in the 79th minute after Newey had been booked for a foul on Mozika.
Ellison took the 30-yard free kick which arrowed its way into the top right corner of the net, leaving Barnes rooted to his line.
Grimsby predictably hit back, but Newey's 20-yard effort in the 82nd minute flashed just wide of the right post, and Ryan Bennett's close range header from a Boshell corner was held by Danby.
Chester punctuated the sustained pressure from their hosts by increasing their advantage three minutes from time when Mozika picked out Ellison with a pass on the left and Ellison's first time strike rocketed its way beyond Barnes and into the roof of the net.
Grimsby spurned their chance to reduce City's lead in the final minute when Boshell screwed his penalty well wide of the left post after he had been fouled by James Vaughan.
Chester finished strongly and saw two shots in stoppage time crash back off the woodwork.
Mark Hughes saw his attempt hit the bar and the rebound from substitute Paul McManus was turned round the post by Barnes.
And McManus smashed a powerful 20-yard strike seconds later that cannoned off the bar.
Ask Davies
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