"Finals are in sight," headlined popular daily tabloid De Telegraaf after Donny van de Beek's early goal on Tuesday night pushed Ajax one step closer to the possibility for the first time in 23 years, AFP reported.
"The road to the Champions League final lies open for Ajax," the paper said, adding coach "Erik ten Hag's eleven in the first half gave a masterclass performance."
"The second half was more difficult... but the only thing the Amsterdammers could be held accountable for is that they did not score more goals to make moot a home game on May 8," said De Telegraaf.
"The Amsterdam fairy-tale is alive and well after a 1-0 victory," the daily tabloid Algemeen Dagblad said.
"Ajax has conquered much of Europe and now also England... where Erik ten Hag treated the football power elites with disdain."
"Ajax can now smell a Champions League final. In the time of oil dollars and extreme broadcast fees this is nothing short of a miracle," it said.
Writing in the De Volkskrant, top Dutch football journalist Willem Vissers said "thanks to a first half-hour of magic Ajax is now close to the Valhalla of club football: The Champions League final on June 1 in Madrid."
But "Tottenham was much stronger in the second half," despite David Neres' rare shot at goal which rebounded off the post.
"Ajax, which against both Real Madrid and Juventus was superior in the second half, dragged itself home with a bit of luck, to the second game on May 8 in Amsterdam," Vissers said.
"The final beckons, but the matter is far from being settled," Vissers warned.
Ajax coach Ten Hag praised his young lions after the Dutch club’s victory on Tuesday.
"A fantastic achievement. We fought like lions," Ten Hag said, Reuters reported.
"We are halfway there and in good shape. The willpower was very nice to see."
Van de Beek was superb and even overshadowed Barcelona-bound fellow midfielder Frenkie de Jong, while 19-year-old captain Matthijs de Ligt showed maturity beyond his years to marshal the defense after the break.
Had Neres not been denied by the post late on Ajax's position would look impregnable, but Ten Hag knows the job is not yet completed.
"I think it's an excellent result for us. We won the game. We are satisfied. We have a very good starting point, but we're only halfway through," he told reporters.
"We can play football in different styles. We can defend very well. We have a team that works together really well; they can fight together really well."
Tottenham manager Mauricio Pochettino, meanwhile, said his team is still "alive" despite the home defeat.
"It's going to be difficult, but it's still open," said Pochettino, BBC Sport reported.
"It's about preparing for the second leg. We will try to win. It will be tough for us, but also tough for them."
History is against Spurs as only one of the 17 previous teams to lose a home first leg of a European Cup or Champions League semifinal has progressed into the final.
"I think the attitude was there, but we didn't find a way to play," said Pochettino.
"We didn't show the energy we wanted to show and the way that we conceded the goal was painful. We struggled in the first half an hour.
"The second half was much better, we forced them to play deeper. We pressed in the way we wanted to press. The second half gave us hope for the second leg."
And the Argentine took responsibility for his side's early struggle, acknowledging that a change of shape from a five-man defense to a back four aided his side.
"I can accept it was a mistake, the shape we used," he told BT Sport. "But there were not too many options. I am not happy – you cannot guess what happens if we play in a different way.
"It was not the shape that conceded the goal. Our approach to the game was not good. I am the manager so I have responsibility."