The two-time defending champions had trailed for much of the match as five- eighth Curwin Bosch slotted seven penalties for the visitors, but they managed to pinch the draw as they hammered away at the tryline for the final few minutes.
Codie Taylor and Jack Goodhue also scored tries for the home side, who moved to 42 points and extended their lead at the top of the New Zealand conference over the Hurricanes (32), who host the Melbourne Rebels on Saturday.
The Sharks remained top of the South African conference as they moved to 28 points, but opened the door for the Bulls to overtake them with a bonus-point victory over the New South Wales Waratahs in Pretoria on Saturday.
Much of the game was stop-start with the Sharks content to kick for territory, put pressure on the home side at the break down and set piece and milk penalties from referee Brendon Pickerill.
All Blacks hooker Taylor scored the only try in the first half when he touched the ball down at the base of the padding on the post after a sustained build up, while Bosch slotted three penalties to give the visitors a 9-7 halftime lead.
Bosch added two more long-range penalties early in the second half as the home side continued to fall foul of Pickerill.
All Blacks captain Kieran Read, who was playing his 150th Super Rugby match for the nine-times champions, then took the team aside and delivered a message for them to lift their intensity.
Read led by example with several storming runs as the home side became far more direct and Goodhue was put over after No.8 gave him a short pass out of a tackle.
The Crusaders, however, kept giving away penalties and Bosch added two more kicks, while missing another, before his side's defence were placed under immense pressure in the final five minutes.
They conceded numerous penalties but it took until the 82nd-minute before Hunt was able to squeeze over and then land the conversion to give his side a share of the spoils.