Cruden, who is in the running for Steve Hansen's All Blacks World Cup squad later this year, limped off in the 19th minute after injuring his left knee.
The 26-year-old had received some treatment on the pitch but could barely put any weight on his left leg and when he tried to change direction while walking he collapsed on the turf again and was immediately replaced by Andrew Horrell.
The victory moved the Chiefs to first in the New Zealand conference and top of the table on 32 points, but they have played two more games than the unbeaten Wellington Hurricanes (31), who play the New South Wales Waratahs on Saturday.
The Chiefs' defensive line speed and work at the breakdown was exemplary as the Hamilton-based side turned what opportunities they had into points.
After Cruden and Tim Nanai-Williams had given the Chiefs a 6-3 lead with two penalties, number eight Michael Leitch pounced on a loose ball that had been dropped by Richie McCaw to score the first try.
Winger James Lowe then intercepted a loose pass inside his own 22-metre area to score after the half-time hooter to give the Chiefs an 18-6 lead at the break, though it could have been closer had Carter not shanked three kickable penalty attempts.
Carter did manage to find his range again early in the second half, while Horrell added a penalty before another Crusaders' error in clearing their goal-line led to Liam Squire scoring the Chiefs' third try. – Reuters
Original source: Chiefs beat woeful Crusaders