LANDOVER, Md. (AP) — The New Orleans Saints had no business winning. Two of their biggest plays were unbelievable flukes, bad mistakes that somehow morphed into positive results. Then they needed the other team’s kicker to miss a 23-yard field goal just to stay alive, and a freeze-frame replay reversal to get the ball in overtime.

But the Saints are living a charmed life these days, and the Washington Redskins are as snakebit as can be. New Orleans trailed by 10 in the fourth quarter Sunday and played more than four quarters without holding a lead — until Garrett Hartley kicked an 18-yard field goal 6:29 into the extra period for a 33-30 win.

‘‘I don’t know about the voodoo, but I definitely believe in destiny,’’ said Drew Brees, who led a no-timeout, 80-yard drive in just 33 seconds to tie the game late in regulation. ‘‘I believe in karma, and what goes around comes around. We’ve been on the other side of this deal probably too many times, and maybe it’s our time, that we start catching some of the breaks.’’

Catching the breaks? That sure explains how the Saints are now 12-0 with the NFC South title in hand. How else to explain a badly shanked punt that turns into a 29-yard gain, or an interception by Brees that somehow becomes a touchdown for teammate Robert Meachem?

‘‘Crazy plays,’’ linebacker Jonathan Vilma said. ‘‘When you’re hot, you’re hot. And sometimes it’s better to be lucky than good.’’

New Orleans also showed it can brave the cold, winning a sub-40 degree game for the first time since 1995. Well, maybe. The defense, led by former Redskins defensive coordinator Gregg Williams, offered minimal resistance, allowing Washington to pile up 455 yards and score 30 points for the first time in Jim Zorn’s 28 games as coach.

‘‘When we do this long enough,’’ Saints coach Sean Payton said, ‘‘you find yourself on the end of wins maybe sometimes that you feel fortunate to have.’’

The biggest number for Washington (3-9) was three — as in the number of consecutive losses in which they’ve blown a fourth-quarter lead.

‘‘I don’t think the best team won today,’’ Redskins center Casey Rabach said. ‘‘We had some bad breaks, some bizarre things happened.’’

Asked if he thought there was any way his team could lose when leading convincingly in the fourth quarter, receiver Devin Thomas said: ‘‘There’s always a way possible — especially with our team — with this little curse we got where we can’t ever get over the hump.’’

So how did it happen? Leading 30-23, the Redskins marched downfield and set up the gimme field goal that would have put the game out of reach. But Shaun Suisham pushed the attempt wide right from a mere 23 yards with 1:52 to play.

Brees went right to work, moving quickly before hitting Meachem wide open over the middle for a 53-yard touchdown with 1:19 to go, essentially sending the game to overtime.

The Redskins had the ball to start the extra period, but Mike Sellers fumbled when he was upended by Chris McAlister after making a catch — a turnover that was only verified after a meticulous replay reversal — giving the Saints the ball at the Washington 37. Brees needed only seven plays to march New Orleans to the 1 before Hartley made the game-winning kick.

Meachem’s first-half touchdown was just a big, but much more unorthodox.

The sequence started when the Saints punted from their own 30. Thomas Morstead shanked the kick so badly that it hit Washington’s totally helpless Kevin Barnes flush on the back near the sideline. New Orleans recovered at the Redskins 41.

Four plays later, facing third-and-26 at the Redskins 44, Brees backpedalled under pressure and threw a desperation pass deep over the middle toward Jeremy Shockey in triple coverage. Kareem Moore dived over Shockey’s back to make an interception, rolled over, got up and ran 14 yards before Meachem simply took the ball away from an upright Moore and started running down the sideline — high-stepping 44 yards for the team’s ninth return touchdown of the season, tying the game at 17 and changing the momentum with 22 seconds left in the first half.

‘‘It was a huge play,’’ Payton said. ‘‘It’s your game changer.’’

NOTES: Brees went 35 for 49 for 419 yards with two touchdowns and one interception. Meachem caught eight passes for 142 yards. … Washington’s Jason Campbell, frequently picking on first-round draft pick Malcolm Jenkins, completed 30 of 42 passes for a career-high 367 yards and three touchdowns with one interception. Thomas had seven catches for a career-high 100 yards and two touchdowns. … The game-time temperature was 36 degrees. The Saints’ previous sub-40 win was Dec. 24, 1995, a 12-0 win over the New York Jets in 33-degree weather at the Meadowlands, according to STATS. … Redskins injuries: DT Cornelius Griffin (sprained knee), WR Antwaan Randle El (sprained shoulder), DT Kedric Golston (sprained elbow) and DT Albert Haynesworth (sprained ankle).