"I am in good form, playing well and feeling good," Klaassen said.
Klaassen, who is running into form after recovering from a long groin injury, scored in the 34th minute, in stoppage time at the end of the first half and then again in the 64th minute before Bojan Krkic rounded off the rout four minutes later.
"We produced great attacks and beautiful goals. It's a shame we didn't score more," Ajax coach Frank de Boer said.
Ajax has to beat AC Milan in Milan on Wednesday to progress to the knockout stages of the Champions League.
Third-placed FC Twente had to wait until second-half stoppage time for the winner in its 2-1 victory at AZ Alkmaar. Roy Beerens gave AZ the lead in just the third minute, controlling the ball on his chest and volleying home from 20 meters before Youness Mokhtar turned the match around with a goal in the 39th minute and the last-gasp winner.