The 27-year-old’s hat-trick, a Davy Klaassen opener and a Robin Propper own goal ensured three points for The Lancers in the matchday 22 fixture at Johan Cruyff Stadium.
The win puts Erik ten Hag’s side on 54 points at the top of the league table, while the opposition are in fifth spot.
Haller, who also set up a goal as well as won a penalty in Sunday’s game, has notched 19 goals and six assists in 19 Eredivisie outings so far this season. He started in each of the matches.
The Ivorian was not the only African in ten Hag’s starting line-up as Morocco right-back Noussair Mazraoui also made the first 11, both men lasting for the duration of the game.
Ghana attacker Mohammed Kudus joined the action four minutes to full-time, coming on for Steven Berghuis, but Cameroon goalkeeper Andre Onana watched the full game from the bench. The Ghanaian was making his first league appearance since sustaining a rib injury last November.
In the Twente set-up was Ramiz Zerrouki who starred for Algeria at the recent Africa Cup of Nations in Cameroon.
Klaassen opened the scoring for Ajax just after the half-hour mark, guiding the ball over the line after Haller flicked on a corner.
In the 53rd minute, the Ivorian turned from provider to finisher, slotting a rebound into the net after a Lars Unnerstall save.
Nine minutes later, the hosts were presented with a good chance to increase their tally but captain Dusan Tadic saw his penalty saved.
Propper then put the ball into his own net in the 77th minute in a desperate attempt to clear Berghuis’ delivery.
Five minutes to full-time, Haller registered his second goal of the day with a cool finish from close range after Antony clipped a ball over the Twente defence.
The Ivorian completed his hat-trick three minutes later with a close-range effort following a Nicolas Tagliafico shot.
Ajax will look to register their 18th win of the season when they face Willem II Tilburg in their next game.