On Sunday, Ten Hag's spellbinding team secured the first leg as it beat Willem II 4-0 to win the Dutch Cup, AFP reported.
The battle with PSV Eindhoven for the Eredivisie title resumes this weekend, and by then Ajax could be through to their first Champions League final since 1996.
Ten Hag's men take a 1-0 lead into their semifinal second leg against Tottenham Hotspur on Wednesday, with young stars like Matthijs de Ligt, Frenkie de Jong and Donny van de Beek mesmerizing Europe on a run that has already seen them defeat Real Madrid and Juventus.
Those players have dominated the headlines, but the work done by the 49-year-old Ten Hag has been remarkable, and entirely in keeping with his progress up until now.
His career as a player was unremarkable by comparison, with the 2001 Dutch Cup the only major trophy he won on the field. The midfielder captained Twente to victory on penalties against PSV Eindhoven.
"He was the captain, he led by example and he always had a lot of confidence," Scott Booth, who played in that Twente side, told AFP.
Booth, a former Scotland striker, scored in the penalty shootout that day. He remembers Ten Hag as "not international class, but a very good club player."
"He was loyal to the club and to his teammates, he loved the game and he loved talking about the game."
Ten Hag was close to Fred Rutten, his coach at Twente, and after ending his playing career aged just 32, he later became Rutten's assistant at PSV.
Prior to that, though, he had a spell as an assistant to Steve McClaren at Twente, helping lay the groundwork for the Englishman to go on and win a first ever Dutch title with them in 2010.
These days, Ten Hag's playing style draws comparisons to Pep Guardiola.
"When we lose the ball, we must win it back immediately," goalkeeper Andre Onana told AFP.
"He is focused on that, he is always telling us that if we have control of the ball, we have the ability to push back any opponent."
In his first season as a coach in his own right, Ten Hag won promotion with Go Ahead Eagles, but he left the club for a job with Bayern Munich's reserve side in the German fourth tier.
His time in Bavaria coincided with Guardiola's first two years as Bayern coach.
"I still remember very well that when I quit the Eredivisie to go and coach in the German Regionalliga, lots of people in the Netherlands were skeptical," he told German daily Bild.
'Winning the lottery'
"I never regretted that decision. To work at a club as big as Bayern, with strong characters like Pep Guardiola or (sporting director) Matthias Sammer was like winning the lottery."
Ten Hag lapped up the opportunity to watch Guardiola's training sessions up close before returning to the Eredivisie with Utrecht in 2015.
After two top-five finishes and a Dutch Cup final appearance, Ajax saw Ten Hag as the ideal man to take over midway through last season when Marcel Keizer was sacked.
Europa League runner-up in 2017, Ajax was knocked out of both European competitions in the preliminary rounds last season, but Ten Hag steered his team to a second-place finish. The foundations were laid for this season's run.
"What he is managing to do with such young players is remarkable," former striker Pierre van Hooijdonk, now a leading pundit, told TV station NOS.
"The likes of De Ligt, De Jong and Van de Beek have only just come out of the academy and are already playing like veterans. Ten Hag deserves huge credit."
If Ajax goes on to win a first treble since 1972, when Cruyff was starring on the field, then Ten Hag will go down as a legend at a club that has had so many great names down the years.
Meanwhile, Mauricio Pochettino challenged Tottenham to seize its unexpected chance to make history as it tries to overturn a 1-0 deficit against Ajax.
Pochettino is convinced Tottenham can still reach the club's maiden Champions League final despite losing the first leg.
Tottenham goes into their biggest game for decades on a low note after losing 1-0 at Bournemouth on Saturday, a defeat that stopped the Spurs wrapping up a place in next season's Champions League via a top-four finish in the Premier League.
Tottenham is three points clear of fifth-placed Arsenal heading into its last league game of the season against Everton on Sunday and a draw will be enough to ensure its return to Europe's elite club competition.
But before that Tottenham, trying to reach its first European final since the 1984 UEFA Cup, has to focus on the challenge presented by Ajax's vibrant young side.
Ajax showed its vast potential against Tottenham in the first leg and should have been further ahead after Van de Beek's opener.
Tottenham improved slightly in the second half, but largely looked toothless without the suspended Son and injured top scorer Harry Kane.
Crucially, Pochettino will have Son back from his ban for the second leg and the South Korea forward should give his team a far more dynamic look.
Pochettino remained upbeat despite the frustration of losing to Nathan Ake's last-minute goal at Bournemouth, and the Tottenham manager hopes his confident attitude transfers to his players against Ajax.
"We have ahead two 'finals' against Ajax and Everton and it's in our hands to be in a good position at the end of the season," Pochettino said.
"No-one believed we'd be in this position in the last week of the competition," Pochettino said.
"We are in a position where it depends on us to be in the (Champions League) final or not and then it depends on us to finish in the top four.
"It's a massive week and that's why we need to move on, try to recover as soon as possible and be ready again but whatever happens I am going to feel proud."