The Sulphurites custodian saved a first-half penalty and also produced five excellent stops to keep his clean-sheet intact and help end his side's three-match losing streak.
Yet, while Belshaw's heroics and a much-improved second half showing from his colleagues can be counted as positives, Town's overall performance will leave manager Simon Weaver concerned.
Up against a Saddlers team who had lost four on the spin at home and not managed a win in 12 attempts, the visitors were completely outplayed during the first period and could easily have been dead and buried by the interval.
The opening quarter was a largely uneventful affair, the first decent opening of the game arriving on 23 minutes when Ryan Fallowfield's deflected cross from the visitors' right was headed over the top by Mark Beck.
The remainder of the first 45 belonged to Walsall, however, with Town indebted to Belshaw for a string of key interventions.
First, the Harrogate number one showed sharp reactions to get down low and keep out Josh Gordon's strike on the turn.
A last-ditch block by the stretching Dan Jones then prevented another goal-bound Gordon effort from hitting the back of the net, before Warren Burrell was adjudged to have clipped Tyreik Wright inside the box.
Emmanuel Osadebe stepped up to take the resulting 38th-minute spot-kick, though Belshaw threw himself to his right and pushed a firmly-struck effort away.
The former Walsall trainee was then quickly off his line to head clear following Burrell's awful attempted back-pass, before thwarting Osadebe once again when the Saddlers attacker took aim inside the box following Liam Kinsella's cross from the right.
Very much on the ropes by this stage, the Sulphurites desperately needed half-time and used the interval to shake things up with a couple of substitutions.
Lloyd Kerry took the place of Warren Burrell in the centre of the park and immediately added bite and intensity, while Josh McPake replaced the ineffective Aaron Martin, as Jack Muldoon was moved up front.
The changes certainly helped, and Town began the second period far better than they ended the first, though in truth, the bar didn't need raising all that high to enable this to happen.
Yet, despite the improvement in their play across the pitch, Harrogate were still reliant on man-of-the-match Belshaw to keep them in the contest.
With 56 minutes on the clock he raced out and spread himself to block superbly from Wright one-on-one, then made a more routine save as he pushed away Wes McDonald's drive from distance.
The Town custodian was at it again moments later, acrobatically diverting a Caolan Lavery shot over the top of his goal.
At the other end, Town managed to engineer a few promising openings, though there was a serious lack of quality about their play in the final third.
George Thomson was well off target with a couple of efforts the edge of the penalty area, while Muldoon wasted the visitors' best opening, slicing a horrible effort high and wide of the mark having driven into a dangerous area following Beck's pass.
Thomson then saw a late free-kick turned over the top by Liam Roberts before pulling an even more useful sight of goal narrowly the wrong side of the upright not long before the final whistle was blown.
Friday's result keeps Harrogate 15th in the League Two standings.
Walsall: Roberts; Kinsella, Clarke, Sadler, Melbourne; Wright (Holden 78), Perry, Bates (McDonald 58), Osadebe; Lavery, Gordon. Unused substitutes: Rose, Norman, Sinclair, Osei-Yaw, Leak.
Harrogate Town: Belshaw; Fallowfield, Smith, Hall, Jones; Thomson, Falkingham, Burrell (Kerry 46), Muldoon; Martin (McPake 46), Beck. Unused substitutes: Minter, Kiernan, Francis, Williams.
Referee: W Finnie (Bedfordshire).