Neil Lennon spoke of an "amazing" night after Olivier Ntcham's dramatic last-gasp winner against Lazio took Celtic into the last 32 of the Europa League with two Group E fixtures remaining.
Striker Ciro Immobile opened the scoring for the home side after seven minutes but Hoops winger James Forrest deservedly levelled in the 38th minute with a terrific finish.
Then, in the fifth minute of added time at the end of a thrilling game, midfielder Ntcham, on for Ryan Christie, finished a counter attack to secure a 2-1 win.
It was Celtic's first win in Italy in 13 attempts and kept them top of their section with a guarantee of European football after Christmas.
The goal also clinched a remarkable double over the Serie A side and Lennon said: "I am so happy and proud of the team.
"Not just winning the game but the way they played the game, the character, the bravery and above all else, real quality.
"It was a Titanic game again, a brilliant game to watch and it was a game we thoroughly deserved to win.
"To come here and play as good as that; this team keeps setting new boundaries. We have qualified after four games. That is unheard of for Celtic in Europe.
"It is amazing night, not just for me, the players, the board and obviously the magnificent support we had in the stadium tonight.
"It is historic. It is a privilege for me to coach these players and work with my backroom staff who do an unbelievable job behind the scenes.
"We are in a good place at the minute. It is job done as far as qualifying for the new year.
"We have a lot of work to do domestically but it is an amazing night for the team and the club."
Asked where it ranked in comparison to Celtic's famous 2-1 Champions League win over Barcelona in 2012 at Parkhead in Lennon's first term as Hoops boss, the Lurgan man said: "It is just behind it.
"To beat Barcelona was a great night and a great achievement for the club but this is almost on a par, to come here and play a team who are in great form, packed with international stars."
With games against Rennes in Glasgow and Cluj in Romania remaining, Celtic have 10 points, Cluj have nine, Lazio three and Rennes one.
Lazio boss Simone Inzaghi said: "There is still hope. Celtic have beaten us home and away so maybe they will be able to beat Cluj in Romania and we have to win against Rennes and Cluj.
"We hit the post, their goalkeeper saved a lot and we also had the referee against us because at 1-1 there was a clear penalty for us that wasn't given to us so it could have changed the game."