The New England Patriots have won three Super Bowls during their dynastic run with Coach Bill Belichick and quarterback Tom Brady. Two of those triumphs came on last-second field goals by their former place kicker, Adam Vinatieri, bolstering his reputation as perhaps the greatest clutch kicker in the sport’s history.

So as the Patriots wind down their preparations to face the New York Giants here in another Super Bowl, it is only natural to wonder if their current place kicker, Stephen Gostkowski, will be up to the task if called upon Sunday night at Lucas Oil Stadium.

“You think about it a little bit,” Gostkowski said this week. “But it’s not like it consumes my every thought. I’m worried about my first kick right now and worrying about having a good game. If it gets down to a situation like that, I’ll be ready. . . . My plan is to stay level-headed throughout the game and towards the end, too.”

The Patriots beat the St. Louis Rams in the Super Bowl 10 years ago, 20-17, on Vinatieri’s 48-yard field goal as time expired. Vinatieri’s 41-yarder with four seconds left gave the Patriots a 32-29 Super Bowl triumph over the Carolina Panthers eight years ago.

Asked this week about Vinatieri’s Super Bowl-winning kicks, Gostkowski said: “Before I got in the NFL, I was a fan like anybody else. Any time games come down to an exciting play, it makes for good TV.”

Gostkowski is a good all-around athlete who was all-state in baseball and soccer as well as in football in high school in Mississippi. He went to college at Memphis on a partial baseball scholarship before walking on to the football team as a place kicker and earning a football scholarship. He was all-conference in baseball and football at Memphis, and the Patriots used a fourth-round pick in the 2006 NFL draft on him.

He has connected on 84.4 percent of his field goal attempts in his six seasons with the Patriots. His field goal accuracy was 84.8 percent this regular season, when he made 28 of 33 tries.

“He’s been doing it for a long time,” Patriots veteran running back Kevin Faulk said. “That’s his job. I’m very confident in him.”

The Patriots’ lone Super Bowl defeat during the Belichick-Brady era was by, of course, three points. The Giants upset them, 17-14, four years ago to ruin New England’s perfect season.

The teams’ current place kickers, Gostkowski and the Giants’ Lawrence Tynes, participated in that game, and Tynes had a 32-yard field goal in the first quarter. But there were no momentous kicks, with the decisive points coming on Giants quarterback Eli Manning’s touchdown pass to wide receiver Plaxico Burress in the final minute.

The Giants also beat the Patriots narrowly, 24-20, in a regular season game this season on a touchdown pass by Manning with 15 seconds to play. So another down-to-the-wire game Sunday certainly seems possible, if not likely, and the place kickers could have significant roles to play.

“I feel like I do a good job not getting overwhelmed by the situation,” Gostkowski said. “Even playing in preseason games are nerve-racking. You’re playing for your job and for a spot on the team. It picks up as the year goes on. But you’ve been doing it all year.”

Of the two place kickers in this game, Tynes enters with a more significant résuméof big postseason kicks. He kicked the Giants into this Super Bowl with an overtime field goal in San Francisco in the NFC title game, just as he kicked them into the Super Bowl four years ago with an overtime field goal in Green Bay in the NFC championship game.

“You make it and you win,” Tynes said this week. “Those are fun. They’re like walk-off homers. Adam has had two in the Super Bowl, which is amazing. Those are fun. That’s the only word to describe it. You get to turn around and see 52 grown men acting like kids again. That’s the best part.”

Tynes was born in Scotland, where his parents met while his father was in the Navy, and moved to Florida as a child. He was a good soccer player who picked up football in high school. After kicking in college at Troy University, he had stints in NFL Europe and the Canadian Football League before spending three seasons with the Kansas City Chiefs and now five seasons with the Giants. He is a career 80.9 percent field goal kicker in the NFL, and was at 79.2 percent during the regular season this season.

In a game with spots in NFL history at stake, the ultimate difference-maker could be Gostkowski or Tynes.

“You think about it,” Tynes said earlier in the week. “We’re at this game. It would only be right if I think about it. Of course a lot of things would have to happen for that to come true. But you have to be ready. I’m mentally prepared for that if it comes down to it. You just have to be ready, take care of your training this week and rely on past successes. Sure, I’m ready for it.”