The home side never looked like getting a positive result after their shot-stopper's early dismissal, and the reigning champions didn't show any mercy
An early red card for home shot-stopper Brian Vandenbussche was followed by Theo Janssen's opener, before Ismail Aissati and a Siem de Jong double made it 4-0 at half-time. De Jong then got his hat-trick after the break to help Ajax to a comfortable victory.
The hosts started the match in disastrous fashion as goalkeeper Vandenbussche fouled De Jong inside the area in the third minute after some sloppy play from Jeffrey Gouweleeuw, leaving the referee no other option but to award the away side a penalty and dismiss the unfortunate glovesman.
Janssen stepped up to take the spot kick and had no trouble finding the net from 12 yards.
Things got even worse for Heerenveen shortly after as again Aissati showed his class. The attacking midfielder picked up a loose ball on the left side of the area, and skipped past his direct opponent before finding the top corner with a powerful left-footed shot to make it 2-0.
Jody Lukoki then should have added his name to the score sheet as well only minutes later after a quick counterattack. However, the winger's placed shot was too weak to trouble substitute keeper Kristoffer Nordfeldt. Ajax did make it three in the 25th minute, though.
Janssen set up Christian Eriksen on the edge of the box, who laid it off for De Jong, and the forward left Nordfeldt no chance with a superb strike from 20 yards out.
Things would only get worse for Heerenveen in the remainder of the game as De Jong doubled his personal tally in the closing stages of the first half after a howler from Nordfeldt, who let the 23-year-old's weak shot slip through his legs.
Unsurprisingly, Ajax continued to dominate play after the interval as De Jong got two good chances to net his hat-trick early on, but the forward fired just wide in the 47th minute before heading just over minutes later.
De Jong would get his hat-trick around the hour mark as he took advantage of miscommunication between Nordfeldt and Ramon Zomer and tapped home from close range to make it 5-0.
Again De Jong and Kolbeinn Sigthorsson came close to adding a sixth, but the former was denied by the upright, while the latter's header bounced off the crossbar.
Heerenveen remain sixth in the Eredivisie table with 54 points from 29 games. The Friezen's next game is the away match versus NEC on Saturday.
Ajax have moved three points clear of second-placed AZ in the table following Wednesday's results. The Godenzonen resume Eredivisie action on Sunday when they host De Graafschap.