It was a soundbite designed to go viral, the kind the ex-pros in the TV studios are always looking to confect; snappy, heavy on hyperbole, bang in the moment. Thierry Henry made it pop on Tuesday night as he interviewed Bukayo Saka on CBS Sports after Arsenal had beaten Atlético Madrid to advance to the Champions League final. “We were the Invincibles. You will be the Unforgettables,” Henry said.

There it was, as laid out by one of the greats, the goalscoring hero of Arsenal’s unbeaten bolt to the 2004 Premier League title, the last one they won.

Saka, who scored the winner in the second leg at a delirious Emirates Stadium, and his teammates can see the path to glory. Actually, it is more than that. It would be immortality. Because if they can hold off Manchester City to win the league and add the Champions League in Budapest on 30 May, it would top anything any group of Arsenal players has achieved.

It is not as if Arsenal are well acquainted with European silverware. The Cup Winners’ Cup in 1994 and the Fairs Cup in 1970 are the extent of their successes. Both competitions are defunct. Henry and his team came closest to winning the biggest of them all in 2006 when they contested the Champions League final against Barcelona.

It remains Arsenal’s only appearance in European football’s showpiece game and a source of eternal regret, especially for Henry, who missed a one-on-one in the early running at 0-0. He also had a presentable opportunity in the second half as Arsenal led 1-0, despite playing since the 18th minute with 10 men after Jens Lehmann’s red card. Again, Henry could not finish. He has said the game still gives him sleepless nights.

Saka & co have the chance to put it right, to make everything so right and it was easy to see Henry’s comment as a passing of the torch or, at least, the potential passing of one. It could all still go wrong. One slip in the league and City could pounce. But Arsenal know it is in their hands. Win the final three games, beginning at West Ham on Sunday, and the title they crave would be theirs.

West Ham are locked in a relegation fight, but there is a reason why they languish in 18th. After that, Arsenal have relegated Burnley at home and Crystal Palace away. Palace are expected to have a Conference League final three days later and, as such, would surely have their minds on that.

It feels like the dream run-in (please read disclaimer in small print) – a little like Arsenal’s draw for the Champions League knockout rounds: Bayer Leverkusen, Sporting Lisbon and Atlético. In other words, no European super-powers. Arsenal earned that, in part, by finishing first in the league phase with eight wins out of eight.

There is the sense of the stars aligning. After all the suffering, particularly from the end of March, all the angst, the mortal fear of falling short, there is greater faith and assurance, a more positive vibe. It has taken hold suddenly because seven days ago, after the first leg against Atlético, the mentality was more akin to that of a siege.

Mikel Arteta railed at the authentically terrible decision to overrule a penalty award that stood to give them a 2-1 lead. The tie ended 1-1, which was a very good result, especially as Arsenal had not been at their best. In the game before that, at home against Newcastle in the league, it was fraught, Arsenal struggling for creativity on their way to a 1-0 win.

Everything changed in the 3-0 victory over Fulham on Saturday – again at the Emirates – with one of the main takeaways being how calm everybody was before and during the game, with the emphasis on the beforehand bit and the early part of proceedings. As against Newcastle, Arsenal scored in the ninth minute, but this time there was no sinking back, no frayed nerves on the pitch or in the stands.

They were remorseless, playing with tempo. They pushed and it did not matter to them that they missed a couple of chances and had a goal disallowed. The certainty was back. It was 3-0 by half-time. Arsenal had scored six goals in their previous eight matches.

It helped that Fulham, whose preparations were affected by a sickness bug, were so poor. But there was an energy about Arsenal, a freshness Arteta noted was down in part to five changes to his starting XI. The biggest boost was the return of Saka after injury. But Riccardo Calafiori’s comeback was significant and then there was Myles Lewis-Skelly in midfield in place of Martín Zubimendi.

It has been a difficult second season at senior level for Lewis-Skelly and Arteta has admitted he has been tough on him. The 19-year-old has had a point to prove. Against Fulham then Atlético, he proved it. On a related point, Declan Rice has dropped back into more of a No 6 role – his old position – and showed why he has such strong support to be named as the footballer of the year.

Arsenal took the feelgood factor of the Fulham game and ran with it into Atlético, the added tonic being City’s failure to win at Everton on Monday. The pre-match scenes were orchestrated to inspire the players, especially the mass welcome by the fans for the team bus on the approach into the Emirates, the smoke from red flares adding to the scene. It was not crazily loud or spine-tingling, but it was, nevertheless, a visual treat.

When it was all over, it was Arteta who led a group of players from one end of the pitch to the other, each of them hand in hand, the adrenaline overflowing. It was hard to remember him looking this happy and it was yet another move by him to whip up the crowd, to create positive energy. They have not all worked in recent weeks. For example, the “bring your lunch” address before the home loss to Bournemouth.

But Arteta sticks at it. This is who he is. He called for “no fear, pure fire” before the second leg against Sporting. He wanted players to “define history” against Fulham. Before the second leg with Atlético, he demanded they were ready to “go out there like beasts”.

The scenes in the dressing room after the victory will stay with everyone who witnessed them, including the Los Angeles Rams head coach, Sean McVay. He was a guest at the game and was invited down after. The challenge for Arsenal is to ensure the momentum is inexorable.

“Sometimes you have these moments in the season where it shifts towards you and everyone has full belief that we can do it,” the winger Leandro Trossard said. “That’s how it is at the moment.”