This is the one. Canucks won all three of their games by a goal and got obliterated in all their losses.
This is the first one that came to mind. People cite it as a great series, but the Canucks weren't close in any of their losses and barely won the games they did win. The series score was ridiculously lopsided.
This may not be a popular opinion, but for me NYR/LA in 2014 felt a lot closer than 4-1. The Kings were clearly the better possession team in the series and deserved their win, but I've always felt that with a bounce or two, the series could have been drastically different. Three of LA's wins came in OT (I believe two in two OT or later). I distinctly remember a Stepan OT post in one of the first two games and a Zuccarello tip off the post in Game Five.