One division separates these two non-league clubs and there was nothing to choose between them on the pitch as Tom Platt saw his first-half header cancelled out by Crellin after the break.
Blue Square Bet North side Harrogate enjoyed the better of the early exchanges, with Dave Merris' shot likely to have caused Hastings goalkeeper Matt Armstrong-Ford more of a problem had it not been slowed by a wet pitch.
Paul Beesley then saw a goal chalked off for a late challenge on Armstrong-Ford before Dee Okojie, with the visitors' first sight of goal, sent his effort just wide. But with half-time beckoning Platt bundled home a corner that Hastings had failed to clear to give the bumper home crowd something to cheer about.
Harrogate sat off in the second half and Ryman Premier League side Hastings took advantage with Crellin firing into an empty net in the 61st minute after goalkeeper Craig MacGillivray had saved well from Bradley Goldburg.
The visitors should have won it late on but Zac Attwood shot straight at MacGillivray when he had the whole goal to aim at.
Matt Rhead's injury-time leveller ensured Mansfield snatched a 3-3 draw at Lincoln.
Rhead climbed off the bench with just six minutes to go and with his side trailing 3-2 but he snatched a replay for the visitors at the death.
The Stags had taken the lead in the 21st minute when Matt Green rounded Paul Farman to give them a deserved lead.
But Alan Power hauled Lincoln level on the stroke of half-time with a glorious 20-yard free-kick after Adam Murray had fouled Jamie Taylor.
David Holdsworth's side then took the lead just after half-time when top scorer Taylor rattled in at the second attempt.
But Louis Briscoe pulled the Stags level just moments later with a blistering 20-yard drive which gave Farman no chance.
In what was a terrific cup clash, Power put Lincoln back in front when he rounded off a searing counter attack but just as Lincoln sensed victory, Rhead powered a header beyond Farman in injury time.
However, the Stags were indebted to Briscoe who cleared a Vadaine Oliver header off the line with the last kick of the game to keep their cup hopes alive.