The Hearts captain, jeered from the pitch by his club's own fans during Saturday's 0-0 draw against Falkirk at Tynecastle which left Laszlo's team in ninth place in the SPL, was the match winner at Celtic Park when he scored the only goal of a dramatic quarter-final from the penalty spot.
Stewart barely celebrated the goal, noticeably turning away from the Hearts supporters.
It was enough to send holders Celtic out of the competition, the misery for Tony Mowbray's men completed when their captain Stephen McManus was sent off in stoppage time. It was Celtic who faced the derision of their own support last night, but a defiant Mowbray insisted he is not concerned by their form which has seen them now lose seven of his 18 games in charge.
For Hearts, it was a first away victory since February. More significant than a place in the semi-final draw for Laszlo, however, was vindication of Stewart's crucial role in his team.
"It was very important for Michael Stewart to show he is an honest guy," said Laszlo. "He is always there for us and I was very happy he didn't miss the penalty. He is one of our most experienced players and you can't buy that.
"It is not only important that we got into the last four tonight, it is important to recognise that. We can't do anything without the supporters, but the supporters can't do anything without us.
"I have always had a good relationship with our supporters. They have always been fantastic, especially last season. Tonight we showed we respect that support. We need the supporters in the bad times as well.
"When we lost 4-0 in Zagreb earlier this season, it was a very bad night and I was very sad for the supporters who went to Croatia. We gave them something back when we won the second leg 2-0 at Tynecastle and tonight we have given the supporters something back again after Saturday's draw against Falkirk.
"Celtic played well, it was an enjoyable game. We had some luck this evening. Two or three times, our central defenders Jose Goncalves and Ismael Bouzid had big misunderstandings. At this level that normally gets punished. But we had good opportunities on the counter attack and both Christian Nade and Andrew Driver should have scored goals. We could have won by more."
Laszlo went into the match against the backdrop of speculation that Ivan Svadovic, a Polish-born former coach of the Lithuanian under-19 international side, is about to be named as Hearts' new sporting director.
The Hearts owner Vladimir Romanov made a flying visit to Edinburgh on Tuesday to address Laszlo and his players, but the head coach took the latest developments in his stride and insisted he welcomed them.
"We don't have any sporting director at the moment," said Laszlo. "If the club like to take one on, they are welcome. For the amount of work I have, I would need three sporting directors. I have no problem with it.
"It is always important for the owner to come and speak to the players and show he is behind us. This happened yesterday and we were all very impressed. Last year, we also had a meeting when we were told what was important. Players can tell any problems they have direct to the owner."
Mowbray, whose team have won just two of their nine home matches since he replaced Gordon Strachan as manager, did not seek any excuses for last night's defeat and claimed Celtic remain on the right track.
"I don't think we can blame bad luck," said Mowbray. "Sometimes you don't get what you deserve. We worked extremely hard, the team were very positive for the vast majority of the game. We kept banging on the door but couldn't knock it down. I'm frustrated and disappointed, but not concerned.
"I would be concerned if we were not making chances. We are making chances in every game. I think we will click. You could see the desire and endeavour to win the game in a stadium that is normally atmospheric. Unfortunately it didn't happen.
"We have to take it on the chin, use the disappointment and take it into the next game. We played very positive football but didn't get what we deserved. I don't see a lack of belief in the team. Give Hearts credit, they defended very deep. But when the chances come, you have to take them. We have to work through it and I believe we will do it."
Asked about the award of the penalty kick, when Christian Nade was fouled by Danny Fox, Mowbray insisted he had "no complaints". Before abruptly ending his post-match media conference, however, he did express bemusement at McManus' dismissal which means he will miss Saturday's SPL match at home to Kilmarnock through suspension.
The big defender was initially booked by referee Craig Thomson for his foul on Andrew Driver, but the decision was changed to a red on the advice of linesman Francis Andrews.
"My only confusion was that is was a yellow first and then a red after the referee had a chat with his linesman," said Mowbray. "But I'm not going to criticise the officials, they were fine."