A second-half red card for Mansfield's James Matthews did not help the Bulls' cause.
The victory kept the Red Badgers just three points behind table-topping Bourne Town and pushed AFC Mansfield to fourth.
Delighted joint-Eastwood manager Martin Ball said: “It’s never an easy place to come, especially after the enforced break we’ve had over the last three weeks.
“Mansfield are a solid side who make you work for everything.
“If we weren’t at it today, we wouldn’t have taken anything from the game.
"I’m delighted with the three points.”
After a three-week break in fixtures, the Red Badgers were eager to get back to competitive action, and a match against their neighbours was the perfect way to restart their campaign.
The opening exchanges were frantic, with both teams struggling to adapt to a rapidly deteriorating pitch that quickly became heavy and unpredictable.
The ball spent much of its time in the air, and passing sequences were frequently disrupted, leading to a game that was far from the ideal spectacle for the purists.
In the 13th minute, Eastwood’s persistence paid off.
Following a corner, Mansfield’s full-back was caught in possession by Danny Elliot, whose quick thinking released Eastwood’s captain, Aaron O’Connor,
He showed a calm head under pressure, chipping the ball expertly to the back post where centre-half Phil Watt was on hand to nod home his fourth goal of a highly impressive debut season.
As the first half wore on, the match remained a scrappy affair with bookings to players from both sides as tempers flared and tackles flew in.
Mansfield were competitive, but Eastwood’s resilience kept them at bay, and the half ended with the visitors holding a slender 1-0 lead.
The second half followed a similar pattern, with neither team able to carve out any real clear-cut chances.
Both sets of players battled valiantly, but the pitch conditions made it difficult for either side to gain control of the game.
A red card for Mansfield midway through the second half was probably the defining moment of the game, Matthews off for a second bookable offence that in truth was probably overdue after a number of heavy fouls throughout the game.
Eastwood made a number of substitutions, looking to freshen things up and ensure they stayed on top.
The decision to bring on Gillies in the latter stages proved to be an inspired one.
In injury time, with Mansfield pushing forward in search of an equaliser, Gillies sealed the victory with a clinical brace.
The first came after a quick counter-attack, where Gillies latched onto a perfect cross from Oliver Robinson and slotted past the goalkeeper with ease.
His second, just moments later, was a carbon copy of his first, this time meeting the cross of Terry Hawkridge to send the Red Badgers home with all three points.
In the end, it was a game defined more by grit and determination than quality football.
Improving neighbours Kimberley MW drew 2-2 away at Newark Town, though remain bottom, and Division One Selston enjoyed a 2-1 midweek away win at relegation rivals Rainworth MW.
On Saturday Kimberley host Belper United while Eastwood are at home to struggling Deeping Rangers and Selston home to Southwell City.