A three-match winless league run saw the Eredivisie champions lose ground on leaders PSV - who have a 12-point lead at the top of the table.
It appeared as though Ajax were set to drop points once more when they were level with the Eagles heading into the final few minutes of normal time.
However, a costly error from goalkeeper Mickey van der Hart, who is on loan at the Eagles from Ajax, in the 88th minute handed De Boer's men a maximum haul.
"The team is fighting, but in a good way," De Boer told Ajax's official website.
"This is the start of an attempt to rise above our poor matches. Anwar El Ghazi's goal [versus Go Ahead Eagles] is an example that shows a bit of confidence and is something good to build on."
Ajax, who drew 1-1 with Twente in October's reverse fixture, could find themselves 15 points off the pace by the time of their match at the Amsterdam Arena as PSV face AZ on Friday.
Phillip Cocu's men have been near unstoppable in the Eredivisie of late, with the club winning 14 of their past 15 league matches - their last loss coming in September.
However, PSV will need to be wary of an AZ side who are five unbeaten in the league and the UEFA Champions League hopefuls can take heart from a 2-1 win in last season's corresponding fixture.
On Saturday, strugglers NAC Breda travel to ADO Den Haag hoping that off-field problems will play no part on it.
It was revealed earlier this week that Milos Zukanovic, a transfer-window arrival from Red Star Belgrade, had appeared for Breda without a required work permit, with the club - who are 17th - now under investigation by the Dutch Football Association.
Also on Saturday, lowly Heracles welcome third-placed Feyenoord, Excelsior host Groningen and Willem II visit Vitesse.
Sunday sees Heerenveen, whose coach Dwight Lodeweges signed a one-year contract extension this week, hit the road to play Cambuur, rock-bottom Dordrecht head to Utrecht, and Zwolle host the Eagles.
