Our midfielder pulled the strings as Slaven Bilic's team impressed in their victory at the Municipal Stadium in Poznan, with Vedran Corluka also playing the full 90 minutes.
Mandukic got Croatia off to great start with a goal after only three minutes before St.Ledger equalised, but further strikes from Jelavic and Mandukic again secured the points.
Luka showed the artistry - particularly in the first half - that we have seen at White Hart Lane for a number of years now, orchestrating Croatia's play and picking passes at will whenever in possession of the ball.
In Group B, Rafa van der Vaart came on as a 71st minute substitute but could not prevent the Netherlands slipping to a shock 0-1 loss to Denmark.
The Netherlands had 28 shots on goal and dominated possession against the Danes, but could not find the net. It leaves Rafa's side facing elimination if they cannot beat their great rivals, Germany, on Wednesday.
"The Germany game on Wednesday is now like a final for us," Rafa said after the match.
"We have two finals but if we lose the first one, we are out of the competition.
"It's a massive game. That's all I can say. We are a long way from the next round but I believe we lost the first game in 1988 and that tournament finished well for us," he added.