The Amsterdam club won 4-1 on the night – 5-3 on aggregate – to reach the quarter-finals at the expense of the record 13-time winners.
And the Serbia international was at the epicentre of the display.
Tadic teed up the opener for Hakim Ziyech, who netted on the run to give the visitors a shock lead at the Bernabeu inside seven minutes.
However, it was his role in the second – which put Ajax on course for the last eight – which set pulses racing.
After sliding past Sergio Reguilon he produced a fabulous turn around Casemiro before storming towards goal.
The 30-year-old then released the ball at the opportune time for David Neres, who rounded Thibaut Courtois to double the advantage.
Formally of Southampton, Tadic would later net a superb third goal with an arrowing shot into the top corner in the second half.
Though Marco Asensio pulled one back, Lasse Schone's fine free-kick completed one of the great European nights in Ajax's recent history since they last won the competition in 1995.
But it was Tadic's second assist which garnered the most attention from a stunning night.
Commentating for BT Sport, former Arsenal defender Martin Keown said: Tadic’s involvement in this goal absolute top class.
"He addresses the ball, the pirouette. He picks out the pass and what a pass it is. Great run as well. That skill is sublime from Tadic.
"Wonderful piece of skill there.
"Was he playing for Southampton six months ago? It is unbelievable the way he is playing here tonight."
Reaction on Twitter also reached fever pitch.
User MH said: "I can literally fap on that Tadic's 360 turn which almost ended Casemiro's whole career."
Mazi Kumar added: "Mad skill from Tadic in the build up to the 2nd goal."
Last June, Saints allow Tadic to leave St Mary's for just £10million.
The fee could rise to £11.4m but based on this display that will be small consolation for the south coast club.
Just over a year ago the midfielder was playing for Southampton in a 0-0 draw against Stoke City.
His spell in England was largely inconsequential, scoring 23 goals in 162 appearances.
However, his display in Madrid means he is now the talk of Europe.
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