By Graeme Bailey
Last Updated: 01/01/70 1:00am
Ronald Koeman's side knew victory was important after title rivals PSV Eindhoven's win on Saturday, and they came out at a rate of knots with Nigel de Jong netting after six minutes.
Ajax did not rest on their laurels, as Victor Sikora doubled the advantage on 20 minutes.
Dutch international midfielder Wesley Sneijder (pictured) made it three before the break and Nicolae Mitea put some gloss on the scoreline with a goal 12 minutes from time.
Feyenoord made sure they did not lose any further ground on Ajax and PSV Eindhoven at the top of the table with a 3-2 win over FC Twente at De Kuip.
The Rotterdam giants took the lead after just 10 minutes when Belgian Thomas Buffel scored.
Dirk Kuyt added a second just before the interval and Buffel made it 3-0 just after the hour.
Twente, without Collins John after his move to Fulham, fought back well and Sjaak Polak (77) and Ramon Zomer (90) both pounced to make for a frantic finale - but Feyenoord held on for maximum points.
Volendam, who sacked coach Henk Wisman during the week, gained a welcome victory at Groningen. Maurice Buys' strike on 75 minutes proved to be the difference between the two sides.
Tom Caluwe's late goal gave Willem II a point from their home game with NAC Breda who thought they had snatched all the points courtesy of Johan Elmander's effort.
Basement boys Zwolle grabbed a point from their home clash with Utrecht. Jasar Takak fired Zwolle in front, but Abdelhali Chaiat's effort secured Utrecht a share of the spoils.