NEW ORLEANS (AP) — Now Drew Brees and the unbeaten Saints can stop talking about emulating Tom Brady and the Patriots.

The way Brees carved up Bill Belichick’s defense in the most lopsided loss New England endured all year, New Orleans can rest assured of its elite status in the NFL, while the Patriots must figure out what went wrong.

‘‘There’s obviously a big gap between us,’’ Brady said. ‘‘It wasn’t nearly as competitive as we all were expecting.’’

Brees threw for a season-high 371 yards and five touchdowns, and the Saints improved to 11-0 for the first time in franchise history with their 38-17 win over New England on Monday night.

Indianapolis is unbeaten, too, making it the first time in NFL history that two teams won their first 11 games in the same season.

Brees stressed that one regular-season win guarantees nothing for a Saints franchise still trying to make its first Super Bowl.

Yet Brees and head coach Sean Payton have talked about following the Patriots’ model for success ever since joining the Saints together in 2006, and the quarterback could not deny that routing them power could give New Orleans a psychological edge it did not have before.

‘‘It only counts for one win on the stat sheet, but emotionally, those types of wins can mean a little more,’’ Brees said. ‘‘Anytime you can win, and win that way, it builds confidence for you.’’

While New England’s 2007 team is the only one to run the table in a 16-game regular season, the 2009 Patriots (7-4) have had their chances to stop the Colts and Saints from trying to do the same.

Only three weeks earlier, New England had the Colts on the ropes, only to lose by a point in the final seconds. That loss will be remembered for Belichick’s attempt to keep Peyton Manning off the field by going for a first down, rather than punt, on fourth down deep in Patriots territory late in the fourth quarter.

Against the Saints, the Patriots were so worried about their inability to keep pace with Brees they went for it on fourth and four from the New Orleans 10 in the third quarter. Brady’s pass for Randy Moss along the sideline was broken up by Mike McKenzie.

‘‘We needed more than a field goal the way that game was going,’’ Belichick said.

McKenzie’s performance was an example of how things are going right this season for a franchise long beset by bad luck or plain bad play. The 12th-year cornerback broke his right kneecap a year ago, finished the season on injured reserve and then was cut. Because of recent injuries in their new defensive backfield, the Saints brought McKenzie back last week. In the first half, he intercepted Brady when the Patriots had a 7-3 lead and in Saints territory, threatening to tack on more.

‘‘This group is very special,’’ McKenzie said. ‘‘I feel honored just to have the opportunity to go out there and play with these guys.’’

Brees was not intercepted and his TD passes went to five different players — 18 yards to Pierre Thomas, 75 yards to Devery Henderson, 38 yards to Robert Meachem, 2 yards Darnell Dinkins and 20 yards to Marques Colston. In doing so, the Pro Bowl quarterback kept New Orleans on pace to narrowly eclipse the single-season scoring record of 589 points New England set in 2007.

He also became the first quarterback to throw for five TDs in a game against the Patriots since Belichick, a defensive guru for decades in the NFL, took over as head coach in 2000.

Brady was making his first appearance in the Louisiana Superdome since leading the Patriots to their first Super Bowl title in February 2002. This time he became the Patriots’ career passing leader, eclipsing Drew Bledsoe’s mark of 29,657 yards in the third quarter, but will have few other fond memories of his latest visit. He was intercepted twice, sacked once, hit as he threw several times and pulled from the game in the fourth quarter after Darren Sharper’s interception.

The Saints were leading by three TDs by then, en route to their ninth double-digit win of the season.

‘‘They were better than we were in every phase,’’ Belichick said. ‘‘I don’t know how to put it any other way. … They were obviously the better team.’’

NOTES: The Saints have 22 interceptions this season, which leads the NFL. Sharper has eight. … New England lost a regular-season game in New Orleans for the first time after winning its previous four. … Saints CB Chris McAlister, signed two weeks ago, played for the first time since having surgery on his right knee a year ago. … The Saints said cornerback Randall Gay had a leg injury but were not more specific.