Strikes from Aaron Martin and Jack Muldoon had Simon Weaver's men on course for a second consecutive victory in as many League Two outings, but Josh Gordon's 81st-minute goal ensured that the visitors returned back to the Midlands with a point.
Playing their first-ever 'home' fixture in League Two at their temporary base - Doncaster Rovers' Keepmoat Stadium - Town didn't exactly get off to the ideal start.
Saddlers frontman Elijah Adebayo's header forced Harrogate stopper Joe Cracknell into action, and from the resulting corner, the visitors took a fourth-minute lead.
A cleverly-worked routine straight off the training ground saw Alfie Bates deliver from the right and pick out Rory Holden, who drilled home a low effort from just outside the home box.
Walsall continued to look a threat when they managed to get the ball in to the rangy Adebayo, though Town were almost level on nine minutes when Martin crashed a header from Warren Burrell's cross against the cross-bar.
With Weaver's men beginning to enjoy more controlled possession, they went close again after Ryan Fallowfield's right-wing cross dropped kindly for Martin, and he was only denied what looked a certain equaliser by Cameron Norman's excellent block inside his own six-yard-box.
Harrogate continued to press and with Fallowfield and George Thomson linking to good effect down the right flank, it came as no great surprise that the hosts' 32nd-minute leveller arrived following a move down that side of the field.
Thomson rolled a pass into the path of the advancing full-back and his low delivery found the near-post run of Martin, who couldn't miss from almost on the goal-line.
Things got even better for Town shortly before the interval. Connor Hall's hanging free-kick from left to right was met by the towering Mark Beck, and his knock-down was pounced upon by Muldoon for 2-1.
The hosts began the second period well enough, Muldoon planting an effort straight at Liam Roberts before Martin was denied by another excellent block from Norman.
The rest of the match would however play out with Walsall in the ascendancy, and for the first time in a long time, Harrogate spent an extended period stuck inside their own territory with their backs to the wall.
Josh Falkingham's loose pass in midfield enabled Gordon to send Adebayo clean through on goal, but despite managing to dance around Cracknell, his attempted finish from a tight angle rebounded off the foot of the near post.
With the Saddlers continuing to turn the screw, Warren Burrell was forced to make a couple of crucial interventions inside his own box before Holden placed a tame effort into the arms of Cracknell when well placed.
The pressure would eventually tell, however, and when James Clarke went down under Hall's challenge inside the away area, referee James Adcock pointed to the spot.
Gordon got very lucky from 12 yards, Cracknell saving his initial penalty, only to see the ball rebound straight back into the path of the visiting attacker, who made no mistake second time around.
Walsall's former Premier League star Danny Guthrie was then sent off for a second bookable offence, and although Town finished with something of a flourish and Fallowfield drew a good save out of Roberts with a 25-yard blast, the final whistle sounded soon afterwards on a contest which neither side really did enough to say they deserved to win.