The two sides will meet again at the weekend in their opening DHL Super Rugby Pacific game.
Hurricanes coach Jason Holland said while he was happy to see his side come back from 10-24 down in the second half to take the win, he would be far happier claiming the winner's points in their next game.
Neither side showed their complete hand, and neither was at full-strength with their All Blacks on return-to-play protocols.
Crusaders coach Scott Robertson said his side created several opportunities that they didn't capitalise on but felt it had been a good contest for them ahead of the season-opener.
The Hurricanes had also offered a reminder of their ability to score from anywhere on the park.
The loss of Moana Pasifika due to Covid issues saw the Chiefs, Highlanders and Blues play a game of three halves, the Chiefs beating both the Highlanders and Blues and the Highlanders beating the Blues.
Chiefs' intensity at the breakdown saw them in trouble with returning flanker Sam Cane sin-binned for repeated infringements by the side.
But their maul defence and scrum power were too good for both opponents.
Highlanders coach Tony Brown said fullback Sam Gilbert had a back issue overnight so was pulled out before the game while wing Rory van Vugt suffered a broken wrist at the end of the first half.
Flanker James Lentjes suffered a neck injury during training last week and was left out as a precaution.
Brown said the game against the Chiefs was what they wanted.
"I felt as though we controlled a lot of that game, we just lacked a little bit of execution at key moments in that game but we were happy around how the boys played and the amount of control we had of that first half," he said.
Against the Blues, they got out to a lead but then lacked the composure to finish the game off when he felt they had been the dominant team.
While he had an idea of his 23 for the opening Super Rugby Pacific game, he said there were some good performances, especially from younger players who put their hands up.
One of the issues to emerge in pre-season play had been the breakdown. Brown said teams looked to be adjusting from the Bunnings Cup rulings that were more of a free-for-all, but he hoped the referees would tighten the breakdown in the first round and allow teams to hold onto the ball for longer.
Scorers were:
Hurricanes 27 (Salesi Rayasi, Julian Savea, Billy Proctor, Alex Fidow, Aidan Morgan tries; Morgan con) Crusaders 24 (Dallas McLeod, Abraham Pole, Macca Springer, Isaiah Punivai tries; Fergus Burke con; Simon Hickey con). HT: 5-12.
Game of three halves:
Chiefs 14 (Emoni Narawa, Pita Gus Sowakula tries; Bryn Gatland 2 con) Highlanders 5 (Scott Gregory try)
Chiefs 17 (Jonah Lowe 2, Tyrone Thompson tries; Josh Ioane con) Blues 7 (Taniela Tela'a try; Harry Plummer con)
Highlanders 21 (Marino Mikaele-Tu'u, Vereniki Tikoisolomone, Folau Fakatava tries; Marty Banks 3 con) Blues 19 (Vaiolini Ekuasi, Josh Goodhue, Taine Plumtree tries, Stephen Perofeta 2 cons).