Frank de Boer's men equalled the current record of four in a row, held by HVV (1900-1903) and PSV (1986-1989 and 2005-2008), by lifting the trophy last season.
However, Vitesse have proved to be a real bogey team for Ajax in recent seasons and the defending champions have now gone four matches without a win in the top-flight fixture, losing three and drawing the most recent in April.
And the Amsterdam club will have to bounce back quickly from a disappointing Johan Cruyff Shield defeat to PEC Zwolle last weekend.
Zwolle produced a second upset over Ajax with a 1-0 win in the season curtain-raiser, having demolished the same opponents 5-1 in the KNVB Beker final in April.
That said, Ajax, who saw captain Siem de Jong depart for Newcastle United in the close-season, have lost four of the last five Shield finals, so it is by no means a reliable marker by which to judge the club's chances in the subsequent league campaign.
Zwolle - fresh from their morale-boosting victory - have the honour of getting the new Eredivisie season under way on Friday when they welcome Utrecht to the IJsseldelta Stadion.
Ron Jans' charges finished 11th last season - matching the achievements of their first campaign back in the top flight a year earlier - but their cup exploits will have made their rivals sit up and take note.
However, a run of one win in 12 matches to finish off the 2013-14 season is a problem that will need to be addressed sooner rather than later.
Feyenoord fell four points short of Ajax last term and visit Den Haag for their opener on Saturday, while Twente - third behind the Rotterdam outfit - travel to Cambuur a day earlier.
Of the promoted teams, Willem II have been dealt the toughest start, with 21-time champions PSV the visitors to Koning Willem II Stadion on Sunday.
Dordrecht - making their return to the top flight after 19 years away - are on the road at Heerenveen, while Excelsior play at NAC Breda.
Elsewhere, Heracles host AZ, and Go Ahead Eagles are at home to Groningen.
