Ajax were dumped out of the UEFA Europa League 6-1 on aggregate by Red Bull Salzburg in midweek, but appear well on course domestically as Twente tripped up.
Quincy Promes had given Twente an 18th-minute lead but a driving run and left-foot finish from Australia winger Tommy Oar shortly after half-time levelled matters.
Relegation-threatened RKC Waalwijk were thrashed 4-0 at AZ Alkmaar.
Jeffrey Gouweleeuw and Nick Viergever scored in the opening 20 minutes before a second-half Steven Berghuis double.
Cambuur Leeuwarden edged four points above the relegation play-off places with a 1-1 draw at FC Groningen.
Elvis Manu's 77th-minute penalty earned the visitors a point after Tjaronn Chery netted first.