Kelly's primary receiver was Miami free safety Louis Oliver, who intercepted three passes and returned one for a record-tying 103-yard touchdown that turned a potential 24-17 lead into 31-10 with 4:38 left in the third quarter.
"One of the great games I've ever seen a defensive back play," said Miami's Don Shula, a former defensive back who has coached in the NFL for 29 years.
Kelly threw a personal record-tying four interceptions. After the first to Oliver, Marino connected with free-agent tight end Keith Jackson for 24 yards and the game's first touchdown.
Marino was rolling and fired to wide receiver Mark Clayton, but Jackson plucked it out of Clayton's path and made a nice run and dive into the end zone. What do you expect after only three days of practice?
"I was throwing to Keith all the way," said Marino, stifling a smile. "And even if I wasn't, I would lie. I would never tell."
"He was looking at me," said Jackson, signed last Monday as a free agent in the wake of the Freeman McNeil antitrust trial. "I don't know if he was throwing to me, but he was looking at me."
It was the first of three touchdown passes by Marino, who defied the largest crowd in Rich Stadium history by calling out audibles and willing the Dolphins to the first win in Buffalo by an AFC East team since 1987.
When Marino is good, he is very, very good. He is now one touchdown pass behind Johnny Unitas. When Kelly is bad, he is very, very bad. Two of his three interceptions to Oliver were ill-advised decisions. Another to J.B. Brown was on a floater.
"I've seen those routes for three years so it's about time I started breaking on them," Oliver said.
Buffalo had beaten Miami 10 of their last 11 meetings and Kelly had his share of success against Oliver. But a 2-4-5 defensive alignment similar to the one used by the New York Giants against Kelly in Super Bowl XXV enabled Oliver to roam and have a field day.
"You can't throw interceptions," Kelly said. "I'm not making excuses for any of the things we did today, including myself. The interceptions, you can say I got blindsided on one, but you've got to look at the whole thing.
"They beat us and beat us good."
The victory kept the Dolphins undefeated at 4-0 and put the Bills in the unfamiliar position of second place at 4-1 in the division they have owned for three years.
The Dolphins scored 24 points after four of the turnovers. The big one by Oliver tied the NFL record set by San Diego's Vencie Glenn in 1987. His 170 yards in returns were second in NFL history to the 177 by San Diego's Charlie McNeil in a 1961 game against Houston.
It was a dream game for Oliver.
"I've been telling the coaches I'd never scored a touchdown in all of organized football -- high school, college, middle school, optimist league, never," Oliver said.
Kelly tried to hit the same route that Oliver had picked off once last year.
"They flood one side and bring two receivers down hard inside and try to hit the outside," Oliver said. "Once I saw two go inside, I just hung there. I run those routes night and day in my head. I couldn't even sleep last night. Every time I'd close my eyes, I got picks for touchdowns."
Once Oliver made his leaping grab, only Kelly had a chance to stop him but failed, injurying his throwing elbow in the process.
Jackson caught four passes for 64 yards playing more than half the game for starter Ferrell Edmunds. After three practices, coaches gave him a written test of 30 questions and he missed only two.
"Contrary to popular belief, there are some jocks who are real smart," Jackson said.
"He has a great understanding of reading coverages and getting into open areas," Marino said. "Today he ran a few option routes and an option is the same here as it was in Philadelphia. We had a small package for him."