Bernie Parmalee and Terry Kirby scored on acrobatic runs and Miami clamped down on Buffalo's injury-depleted offense for a 23-6 victory Sunday.
"The urgency of winning was extremely important, but it should be like that every week," Marino said. "That's the lesson we've learned the past two weeks."
Marino sat out both games because of hip and knee injuries.
The victory was Miami's first over Buffalo at Joe Robbie Stadium since 1990.
"They won an important game that they needed to win to stay alive," Bill defensive end Bruce Smith said.
Miami's losing streak amid high expectations prompted criticism by fans and the media, much of it directed at Don Shula. The 65-year-old coach celebrated Parmalee's go-ahead touchdown in the third quarter with uncharacteristic animation, running along the sideline.
"I've been coaching a long time," Shula said. "Despite what some people have said the last couple of weeks, I put everything into it. I work hard and do the best job I can do. Nothing I do is contrived. It's me. What you see is what you get."
Marino completed 20 of 35 passes for 232 yards with no touchdowns. His biggest plays against the AFC's best defense were two handoffs. Parmalee scored on a 20-yard run in the third quarter to break a 6-6 tie, and Kirby added an 11-yard touchdown dash.
Parmalee rushed for 83 yards and Kirby 60. Miami converted 10 of 18 third-down situations and had an advantage of nearly 13 minutes in time of possession.
The Dolphins' domination made their losses to Indianapolis, New Orleans and the New York Jets that much more galling.
"This team should be 8-0," Marino said, "but that's in the past."
Buffalo assistant head coach Elijah Pitts fell to 0-2 while filling in for Marv Levy, who is recovering from surgery for prostate cancer.
With Thurman Thomas and Andre Reed sidelined because of hamstring injuries, the Bills' offense sputtered. Eight of their 11 possessions failed to produce a first down.
Thomas' replacement, rookie Darick Holmes, rushed for only 24 yards in 12 carries.
"They were missing two people who are a big part of their offensive performance," Dolphin linebacker Bryan Cox said. "We were supposed to pound them."
They pounded Jim Kelly, who threw for only 147 yards and was sacked twice. He sat out Buffalo's final series.
"It's real hard to move my neck and my shoulder's sore, but I'll be all right," Kelly said.
"Today was just way, way, way too many mistakes. Mental mistakes can get you killed. Mental mistakes almost got me killed."