Harry Pritchard's goal for the hosts shortly after half-time made it a nervy second-half.
With Solihull beating Bromley, a win was a must here for a top three place to remain in Halifax's hands. It wasn't pretty, but The Shaymen got what they came for.
The Shaymen settled quickly and were calm and composed in possession, which they had plenty of early on.
Eastleigh soon found their feet though, after which the teams cancelled each other out in an uneventful contest.
The only efforts at goal in the first half-an-hour were from Jordan Slew and substitute Sam Smart, both of which were harmlessly off target.
This was two sides who wanted to play patient, progressive football but weren't executing it well enough to breach the opponents' defence.
The best bit of quality in the first-half saw a one-two between Jack Senior and Billy Waters, from which Senior's right-foot shot was deflected over for a corner.
From that, Spence was given too much time on the edge of the box to pick his spot with a superb strike.
Eastleigh then had a penalty appeal turned down for a coming together between Senior and Smart.
The Shaymen, whose only change from Saturday was Matty Stenson starting in place of Harvey Gilmour, had looked the more comfortable team in possession during the opening half. When they'd come under pressure with the ball at the back, they'd been able to evade challenges, but the hosts were caught in possession on the edge of their own box by Waters, and Warburton kept his cool to finish low past the keeper from 10 yards.
A goalbound shot from the hosts was blocked inside the Halifax box as The Shaymen reached half-time with their two-goal cushion intact, and with 11 players, as Spence was only cautioned for a poor tackle on halfway which sparked a huge melee, after which Pritchard and Jesse Debrah were also booked.
Sam Johnson was the sole survivor from Town's only previous win here back in 2019, but he'd had no shots to save until Pritchard converted a low cross from the right by Smart not long after half-time to get the hosts right back in it.
There was more bite and aggression from Eastleigh after the interval, while Town weren't as smooth or assured on the ball.
The hosts were unable to build much pressure or momentum though, with Town working hard off the ball to keep the hosts at arm's length, but not creating much themselves.
Warburton fired wide from 20 yards for Town, Michael Kelly's free kick went just over for Eastleigh.
The score remained the same, but the tension increased in a finely-balanced contest.
Eastleigh went close in the 88th minute when substitute Ronan Silva curled a shot inches wide, but the hosts couldn't produce enough quality when it mattered to score again.
Eastleigh: McDonnell, Camp, Boyce, Broadbent (Smart 20, Silva 76), Kelly, Smith (Pitman 76), Miley, Pritchard, Harper, Hesketh, Whitehall. Subs not used: Bragg, Barnett.
Scorer: Pritchard (48)
Shots on target: 2
Shots off target: 6
Halifax: Johnson, Warren, Debrah, Bird, Senior, Green, Spence, Slew, Warburton (Woods 77), Stenson (Gilmour 62), Waters (Dearnley 84). Subs not used: Benn, Cooke.
Scorers: Spence (39), Warburton (42)
Shots on target: 2
Shots off target: 4
Referee: Daniel Lamport
Attendance: 3,068 (164 away)
Town man of the match: Kian Spence and Jesse Debrah both contenders, but I'll plump for Jordan Slew. Used the ball intelligently, looked a threat and did his share of defensive work too.