I'll add one more. 1996 Western Conference Finals, with the 62-13-7 Detroit Red Wings hosting Colorado.
Now, for those who don't remember, Quebec was a team that exploded onto the scene in 1992-93 after some hideously bad years. They had a 2-0 series lead against Montreal that year before dropping four straight, and in 1994-95 they had the NHL's best record but lost in the first round to the 8th-seeded Rangers. There were serious questions about whether this team had the tenacity to win in the playoffs; the skill was clearly there.
Detroit had the league's best record by 27 points, a +144 goal differential, the best penalty kill by a mile, the second-best power play, top defense...you name it. And they're broken through the previous year by making it to the Cup Finals before being swept by New Jersey.
Game 1 opened with Detroit taking a 1-0 lead and pressing while on the power play, looking to make it 2-0. Instead, Stephane Yelle led a rush the other way, and this happened.
Colorado would win Game 1 in overtime, then took Game 2 en route to a 4-2 series win and Stanley Cup. But it may not be an exaggeration to suggest that it really began with this: a soft team with a bad reputation getting a huge momentum-changing play early and starting to believe that they could beat the record-setting team.