Despite Harrogate’s threat from long balls and set pieces it was the hosts that had the better opportunities in the first half. First, Belshaw made a save from a Josh Gordon strike before denying Emmanuel Osadebe from the penalty spot.
He went on to save another Osadebe effort before then saving a one-on-one chance in the second half from Tyreik Wright.
Harrogate had opportunities of their own in an entertaining game but it was Belshaw that made the biggest stops to deny Walsall a much-needed victory.
Dutton made two changes to his Walsall side as he moved to a 4-4-2 formation.
Alfie Bates replaced Stuart Sinclair in midfield, while Wright returned to the line-up and Tom Leak dropped to the bench.
Liam Kinsella kept his place in the team playing at right-back, meaning Cameron Norman was again among the substitutes.
Callum Cockerill-Mollett lost his place in the squad and was replaced by Rory Holden who was involved for the first since mid-December after suffering a serious knee injury. He made the bench.
Jack Nolan and Frank Vincent were also left out of the squad, while Dan Scarr was out with an injury. Hayden White was completing the final game of his suspension.
Simon Weaver also made two changes to his side as they stuck with their 4-4-2 formation.
Ryan Fallowfield and Mark Beck came into the team. Harrogate only named six substitutes.
Within the first minute of the game Wright looked bright and broke inside the pitch towards goal. His shot was tame and wide but he showed an early intent.
Meanwhile, striker Aaron Martin was fortunate to escape without at least a yellow card after a late and high tackle on Max Melbourne. The incident came within the first five minutes of the game.
The opening 10 minutes came and went without any big chances for either side. The visitors were having more joy, however, by playing long balls forward to towering striker Beck who was regularly winning the first ball.
Walsall were appealing for a penalty when Caolan Lavery went down under a challenge from Dan Jones. Referee Will Finnie was unmoved.
Minutes later Beck directed a free header wide from less than 10 yards. The striker could have done better.
The Saddlers would have taken through Gordon if not for some magnificent goalkeeping from Belshaw, who is a former Walsall academy player. Osadebe played a superb dinked pass into the striker who chested it down and took aim on the half-volley. His effort was destined for the bottom corner before Belshaw flung out an arm and clawed the ball away.
With Walsall well on top, two hectic minutes should have seen the hosts take the lead. First, Wright was beaten to a loose ball by Belshaw, but his clearance fell to Gordon. The striker took aim at an open goal but saw his effort blocked by Jones.
From the resulting corner Wright was brought down in the box and the referee pointed to the spot. Osadebe stepped up but saw his effort saved well by Belshaw to his right.
Osadebe was then thwarted by Belshaw again on the stroke of half-time. Kinsella did superbly well to nick the ball from Jack Muldoon, get to the byline and cut back for Osadebe. His first-time shot from the edge of the box was saved well.
Despite a lacklustre start to the half Walsall entered half-time having improved drastically in the second period of the first 45. Belshaw kept the visitors in it, however, and the sides ended the half drawing 0-0.
Harrogate introduced Lloyd Kerry and Josh McPake at half-time in an effort to get a foothold back in the game.
Those changes seemed to help as the visitors looked far brighter than their poor end to the first half. McPake crossed low and a neat flick at the near post from Jones was just wide.
Despite that, the next golden chance again fell to Walsall. A lovely reverse through ball from Lavery put Wright one-on-one with Belshaw, but again the goalkeeper saved his team, stopping the shot with his legs.
The hosts then made an attacking substitution by bringing off Bates, moving Osadebe into midfield, and bringing Wes McDonald on to the left wing.
In what was starting to become an open back-and-forth game Beck then saw a goal-bound effort blocked by James Clarke.
A handful of Saddlers efforts then came and went as McDonald, Osadebe and Lavery all had shots saved.
For all of Walsall’s chances Harrogate were still dangerous with the long ball. Beck did well to flick one on to Muldoon who set up George Thomson, but his shot was well wide. Muldoon then blazed wide an effort of his own.
After 78 minutes Holden made his long-awaited return from injury, replacing Wright.
Some late danger saw Liam Roberts tip over a Thomson free-kick as the game entered injury time. The midfielder then shot just wide minutes later.
In the end the teams took a point each as neither side could find that all-important winner.
Walsall: Roberts, Kinsella, Clarke, Sadler, Melbourne, Wright (Holden, 78), Perry, Bates (McDonald, 58), Osadebe, Lavery, Gordon.
Subs not used: Rose, Leak, Norman, Sinclair, Osei Yaw.
Harrogate: Belshaw, Fallowfield, Smith, Hall, Jones, Thomson, Burrell (Kerry, 45), Falkingham, Muldoon, Martin (McPake, 45), Beck.
Subs not used: Minter, Kieran, Francis, Williams.