The seven-times champions lost to the Wellington Hurricanes last week and defeat to the championship-leading Chiefs in their penultimate match on Friday would almost certainly leave them without a place in the playoffs for the first time since 2001.
Carter was recalled at fly-half after recovering from a hamstring injury to take back the kicking duties after replacement back Tyler Bleyendaal missed what would have been a match-winning penalty from halfway last Saturday.
Number eight Reed, who has been in storming form for the Crusaders and New Zealand this year, has been cleared to play after a concussion, allowing Richie McCaw to return to his favoured position on the openside flank.
Dagg missed last week's match with an ankle injury but will bring his attacking flair back to the team at full-back for the match against the Chiefs, who would wrap up the New Zealand conference title with victory this weekend.
"We really missed that experience last weekend," Crusaders coach Todd Blackadder told local media.
"When you look at the way they had been performing before injury, they were absolutely on fire. It's great to have them back."
The Chiefs have brought a big gun of their own into their starting line-up side for Saturday's clash with aggressive Tongan prop Sona Taumalolo, who is the team's top try scorer this year, taking his place at loosehead.
Hulking number eight Kane Thompson has been ruled out by a back injury but Sam Cane gets his first start at openside flanker since making his All Blacks debut in last month's test series against Ireland.