They won because they understood their role. They didn't lose the game for their teams, at least in the Superbowl years. Marino was a great passer, but the offense was geared to him. He appeared in one Superbowl game and couldn't win. I always questioned Marino's judgement and leadership ability. Marino was about personal achievements and amassing individual stats. He was a loser.
Here's an interesting trivia question: Who were Andra Franklin, Woody Bennett, Tony Nathan, Lorenzo Hampton, Troy Stradford, Sammie Smith, Mark Higgs, Bernie Parmalee, Karim Abdul-Jabbar, and J.J. Johnson?
Answer: In addition to being pretty inconsequential NFL running backs during their careers, they were also the players who led the Dolphins in rushing during Marino's 17-year career. There was a single 1,000-yard rusher among them (Abdul-Jabbar in 1996) and a single Pro Bowler (Keith Byars in 1992, who isn't even on this list because he was primarily a receiver at the RB position).
If you go back over the first 14 or 15 years of their careers, you'll find that John Elway and Dan Marino were very similar. They were the dominant offensive players on teams with mediocre running games, but they never won any championships. I find it hard to believe that Elway should be considered a better quarterback than Marino just because an old, broken-down Elway had Terrell Davis on his team for the last two years of his career.