The Chiefs scored four brilliant tries to Tim Nanai-Williams, James Lowe, Kane Hames and Aaron Cruden, but they only converted two of them to give the Crusaders the breathing room the needed.
The Crusaders, who produced several comeback victories earlier in the season, kept the Chiefs pointless for much of the second half with the Hamilton-based side actually holding a 17-13 lead after a highly intense first half.
The victory was the second in successive weeks for the seven-time champions against tough New Zealand sides and sent a strong message to the rest of the competition they would be tough to beat during the business end of the season.
The test-match intensity was evident again at the National Stadium in Suva, with the Chiefs dominating the early phases of the game with a high-octane attack, however, Crusaders' flyhalf Richie Mo'unga gave his side an early 6-0 lead with two penalties.
The Chiefs then struck back with two brilliant tries to Nanai-Williams and Lowe, neither of which were converted, before Bedwell-Curtis stormed over following a brilliant break by Crusaders centre Jack Goodhue.
Mo'unga added his first conversion before Chiefs' prop Hames barrelled over to give his side their halftime lead.
The Crusaders, however, quickly overturned the deficit with Havili finishing off a sweeping counter-attack before Funnell crossed with just over 20 minutes remaining to give his side a 25-17 lead.
Mo'unga extended the lead with his third penalty before Cruden then crossed following a solid attacking scrum with less than 10 minutes left to give his side the opportunity to steal a late victory.
The Crusaders flyhalf, however, added his fourth penalty before the Chiefs wasted two attacking lineout opportunities with poor throws to end their hopes.
(Reporting by Greg Stutchbury in Wellington; Editing by Amlan Chakraborty)
