And the experience nearly ruined their trip to London in 2007.
A streaking Giants team that had won five straight played an 0-7 Miami team during that Super Bowl season, and Tom Coughlin's team ended up escaping with a 13-10 win.
Four seasons later, the two teams meet again with the 0-6 Dolphins looking for their first win at the Giants' expense.
The Giants (4-2) understand they cannot afford to take the Dolphins lightly or get caught looking ahead to next week's game at New England, which starts a daunting stretch of the Giants' schedule.
"They've played in a lot of tight games," quarterback Eli Manning said of the Dolphins. "They could easily have several wins to their record right now. A lot of games coming into the fourth quarter and the opposing team just made some big plays to get wins. They play extremely hard. They have talent on both sides, and it's just a matter of we have to play smart football and know that we have to have a great day of execution and go out there and play well."
The Dolphins have lost all their games by an average of 9.3 points per game. They are coming off a stinging 18-15 overtime loss to the Broncos in which they blew a 15-point lead in the final three minutes of regulation.
The Dolphins play hard but are still looking for some breaks to go their way.
"Do I believe in luck?" Miami coach Tony Sparano asked. "What's interesting is I am one of these guys that goes out jogging before games, and last week I found a penny face up in the stadium while I was working and that didn't work. I am not quite sure I believe in luck a whole lot at this second."
While the Dolphins are firmly in the Andrew Luck sweepstakes for the first overall draft pick, the Giants are looking to take care of business before their schedule becomes an uphill grind.
After the Dolphins, the Giants enter a six-game stretch in which they face four division leaders: New England (5-1), San Francisco (5-1) and New Orleans (5-2) on the road, and defending champion Green Bay (7-0) at home. Right in the middle of that stretch is a rematch with the Philadelphia Eagles.
But first, the Giants must keep Miami winless.
"Right now, their back's against the wall, so it's tough to go against a team like that," linebacker Michael Boley said. "[This game is] a stepping stone to where we want to be. For us, right now we can't afford to let up."
The Giants cannot suffer a letdown at home like they did when they dropped a 36-25 loss to Seattle at home on Oct. 9. Those are the types of losses that come back to haunt a team at the end of a season.
The Giants also would like to get off to a quick start. Their past four games have gone down to the fourth quarter, with the Giants pulling out three of them.
"'Respect all and fear none' is the approach we take," Coughlin said. "What we are trying to do is be concerned with our team, and making sure that our team plays and takes our execution to another level. We want to eliminate any lull in our play and continue the concept of not turning the ball over."
This season, teams appear to be in a lull upon returning from the bye. Teams are just 3-9 coming off byes after the new CBA-mandated four-day break for players during bye weeks.
The Giants are coming off their bye but have been successful under Coughlin in that situation, having won three straight and four of their past five games that have come after the bye.
And they are nearing full strength, as all the players on the roster practiced for the first time this season Wednesday. Defensive end Justin Tuck (groin/neck) and running back Brandon Jacobs (knee) hope to play Sunday barring a setback.
And first-round pick Prince Amukamara is nearing a return from a broken foot.
The Giants are eager to see what they are capable of doing at full strength with a pass rush that could include Tuck, Osi Umenyiora, Jason Pierre-Paul, Mathias Kiwanuka and Dave Tollefson for the first time this season.
The Giants would like to get as much pressure on quarterback Matt Moore as possible. Moore, who will play despite nursing an injury to his ribs, has split games against the Giants in the past two seasons.
In 2009, Moore quarterbacked Carolina to a 41-9 rout over the Giants in the final home game at Giants Stadium. He completed 15 of 20 passes for 171 yards and three touchdowns.
But in 2010, Moore completed just 14 of 33 passes for 182 yards and one touchdown while throwing three interceptions in a 31-18 loss to the Giants. Moore was sacked four times in that season opener.
"It doesn't matter who the quarterback is; we have to go out there and impose our will on them," cornerback Corey Webster said. "We are going to do what we were taught to do and trained to do, which is pressure the quarterback, get hits on him, try to get some sacks and turn over the ball. That is all we can control."