The visitors found a second in the dying moments to rule out Liam Henderson’s brace.
Sean Reid’s free-kick was swatted away well by Dan Haystead in the opening stages, before Henderson couldn’t win the rebound.
Liam Murray then fired a low chance into Haystead’s grip on 13 minutes after cutting inside from Reid’s pass.
Grantham’s first chance came three minutes later, as Jonathan Wafula hooked a promising free-kick over from a promising position.
The Hornets had a great opportunity with 26 on the clock as Oliver Walters’ cross was misjudged by Haystead, however Murray could connect fully with an open goal in sight.
The Gingerbreads took a foothold on the game, and Kieran Hayes went down from Walters’ tackle but the referee dismissed the penalty appeals.
As the half came to end, Grantham top scorer Harry Wood was sent off for sliding down Murray.
Four minutes into the second period, Matt Chatfield's side won a penalty after Robbie Spence's misplaced pass was picked up by Wafula, before Tom Devitt took down Nathan Tyson.
Centre-back Ashton Hall stepped up to give Grantham the lead, sending Shaun Newbrook the wrong way.
Hebburn responded positively and caused a goal line scramble as Murray's strike was blocked, before Spence smashed the rebound wide.
Henderson stuck Hebburn back on level terms after pouncing on a weak back pass and prodding past Haystead at close-range on the 57 mark.
James Harrison nearly made an instant impact after coming off the bench, with Reid taking down Joe Walton's cross before the forward was denied by Haystead.
Arron Thompson's resulting corner was met by Devitt, who nodded past the near post on 67 minutes.
Harrison had another opportunity after racing to keep the ball in at the byline, but his cross-come-shot was held by Haystead.
Daniel Moore's outfit went in front on 81 as Walton's ball was chested by Henderson before he swung a sublime effort into the back of the net.
Lee Shaw made it 2-2 on 90 minutes after sticking past Newbrook at point-blank range.
Hebburn's best chance in injury time saw Murray's set-piece cleared into the air, where Henderson headed off the far post.
Hebburn Town: Newbrook, Walton, Donaghy, Devitt, Walters (Harrison 63'), Thompson, Spence, Phillips, Reid (Moore 79'), Murray, Henderson
Subs not used: Coulson, Bada, Field
Goals: Henderson (57’, 81’)
Yellow cards: Walters (20'), Henderson (37') Donaghy (47')
Grantham Town: Haystead, Tootle, Tait, McCrory, Wright, Hall, Shaw, Hayes (Jemson 82'), Wafula, Wood, Tyson (Sherlock 75')
Subs nots used: Tuntulawana, Leslie, Cocks
Goals: Hall (50’), Shaw (90')
Red cards: Wood (45+4’)
MOTM: Liam Henderson
Referee: Kieran Downey
Attendance: 210