Town remain seven points clear of the National League relegation zone, but the point will prove useful in keeping relegation-threatened Solihull Moors at arm’s length.
The Shaymen lacked the intensity and energy they’ve shown so far in the unbeaten run they’ve put together since Fullarton’s arrival, but they still had the best chances, with Mike Fondop-Talom missing two clear-cut opportunities to break the deadlock.
Halifax displayed more attacking intent than the visitors and really started to build some momentum by the midway point of the first-half, with Ben Tomlinson and Matty Kosylo both going close before a superb one-two between Connor Thomson and Jacob Hanson set the full-back away down the right, only for the ineffective Thomson to miss his kick trying to connect to the cross.
An awful error by Solihull defender Fiacre Kelleher let in Fondop-Talom after half-an-hour, but after racing clean through on goal, the striker blazed over.
Adi Yussuf then squandered a great chance when he blasted over from inside the si- yard box.
Matty Brown headed Jake Hibbs’s corner against the post with 20 minutes remaining, before Fondop-Talom had a glorious late chance to make amends for his earlier miss.
But, after he was found after a superb run by Kosylo, his shot from eight yards was well-saved by Max O’Leary.
“If you’ve seen the game and seen the result, I don’t think it is a classic 0-0 that you would expect,” said Fullarton afterwards.
“Obviously from our point of view, throughout the game we were looking to win it and I don’t think there was any doubt. We had a game plan which would get us into a position to win the game and we followed that.
“On numerous occasions, we had those opportunities.
“Of course, we have to do better when we create these chances, but I think the reaction of the fans and the general feel about the place, it was a good game to watch.”
Guiseley’s game at Torquay United was postponed due to a waterlogged pitch.
FC Halifax Town: Johnson, Hanson (Graham 54), Brown, McManus, Wilde, Thomson (Hibbs 70), Hotte, Collins, -Kosylo, Tomlinson, Fondop-Talom. Unused substitutes: Nicholson, Oliver, Denton.
Solihull Moors: O’Leary, Kelleher, Williams, Carline, Daly, Carter, Sterling, Reckford, P Green, Yussuf (Hylton 62), Thomas (Reid 76). Unused substitutes: K Green, Lait, Martinez.
Referee: Marc Edwards