And City almost grabbed their second win in a week 13 minutes from time when Michael Branch put Robbie Foy clear, but with the goal at his mercy the Chester striker fired wide.
Mansfield, without a win in six games, have now scored just eight goals in 14 home games and after an encouraging first half faded badly.
The Stags, minus five injured first-team players, created the first chance in an open start when Richie Barker shot wide after good work by home debutant Giles Coke, before Scott McNiven's piledriver was palmed to safety by the diving Chris McKenzie.
In the 23rd minute a curling free-kick from Adam Rundle just evaded three strikers as the home side failed to turn their superiority into goals.
On the half-hour, as the rampant Stags again penned Chester in their own half, it needed a last-ditch tackle by Phil Bolland to deny Fraser McLachlan a goal.
McLachlan found himself unmarked in the six-yard area on the end of another dangerous Rundle cross, but his point-blank drive was somehow deflected over by the lunging Bolland.
City finally tested home keeper Kevin Pilkington eight minutes before half-time when Richard Hope's header from an Andy Nicholas long throw was tipped to safety from under the bar.
Then Foy's fierce shot was beaten away by the keeper after a McNiven error.
Another poor defensive mistake, this time by Jake Buxton, gifted Ryan Lowe another opportunity on the hour. However, Pilkington again came to Mansfield's rescue with a fine save at the second attempt.
Fifteen minutes later Foy drilled that golden late opportunity wide as City carved out the better second half chances on the break.