Crotty combined with Carter in a glittering partnership to score a try in each half, and the New Zealand flyhalf helped himself to another as the home side tore the Reds' defence to shreds on a chilly night at AMI stadium.
Winger Tom Marshall scored a fourth try as the Crusaders set up a last-four showdown with either the defending champion Chiefs in Hamilton or the Bulls in South Africa.
Carter, in majestic form at the business end of the season, came off 10 minutes early after a dominant 20-point game, shortly after the crowd welcomed back All Blacks captain Richie McCaw, who came off the bench for his first Super Rugby appearance this season after a long sabbatical.
The Crusaders' next opponents will be decided by the second qualifying final on Sunday, when the ACT Brumbies host the Bloemfontein-based Cheetahs in Canberra.
A win for the Brumbies would send them to South Africa to face the Bulls in the semi-finals, leaving the Crusaders to face the Chiefs in Hamilton. If the Cheetahs manage an upset, they would go to New Zealand while the Crusaders would make the long trip to Pretoria.
The Crusaders, seeking a record eighth title in the short history of the southern hemisphere competition, will have little reason to fear whoever they face next weekend, having smashed both the Chiefs and Bulls during the regular season.
The Reds defeated the Crusaders for their maiden Super Rugby title in 2011, and came into the match talking tough about breaking a win drought in Christchurch dating back to 1999.
Within 11 minutes they trailed 10-0, and headed into the halftime beak down 21-6, demoralised after being smashed at the breakdown and cut to pieces by the Crusaders' jet-heeled backs.
The visitors' scoring was confined to three penalty goals to New Zealand-born Quade Cooper, who was jeered by the Christchurch crowd with every touch of the ball and completely outclassed by opposing flyhalf Carter.
Carter slotted the first of his three penalty goals to open the scoring in the third minute and set up Crotty with an inside pass to allow the bustling centre to canter under the posts in the 10th minute.
Carter was later the beneficiary of a brilliant team try at the stroke of halftime, set up by a barnstorming run by lock Sam Whitelock.
Whitelock's dart to the Reds' 22-yard line allowed scrumhalf Andy Ellis to shoot a long ball wide to winger Zac Guildford, who gave off in turn to Carter, the flyhalf fending off a weak tackle before crossing at the left corner.
Cooper put the Reds within two converted tries with his third penalty kick shortly after the re-start, but the Crusaders hit back immediately with another breathtaking team try.
The dangerous Israel Dagg flicked a quick pass in close to put Wyatt Crockett thundering toward the line, and the prop dished off to flanker Matt Todd, who fed winger Tom Marshall for the Crusaders' third try at the left corner.
Carter emerged again late in the game to complete the rout, breaking the Reds' line deep at the right wing and offloading to Crotty for the centre's second with 13 minutes to play.
The Reds' humbling loss was coach Ewen McKenzie's last game in charge before he takes over the reins of the Wallabies, and the former test prop will have a lot to ponder before Australia's opening match of the Rugby Championship against New Zealand next month.
The Crusaders shut down Cooper, who many have backed to reclaim the Wallabies' starting flyhalf spot, and dismantled the Reds' running game to the point that coach Todd Blackadder felt relaxed enough to leave talisman McCaw cooling his heels on the bench until the game was effectively decided.