INDIANAPOLIS — The New Orleans Saints opened the season operating with a very slight margin for error, a razor-thin line for a rebuilt roster trying to establish an identity as it tried to weather a rash of early injuries and the growing pains of a young club.

Now, that margin for error is starting to grow.

Working behind an opportunistic defense that staked it to an early lead for the second week in a row Sunday, New Orleans survived a furious Indianapolis rally and a handful of its own miscues to pick up a 27-21 win over the Colts. The Saints posted their third win in the past four games and their first of the season on the road.

“I think we’ve identified some things offensively, defensively that we’ve been able to kind of fine-tune and establish our identity with,” quarterback Drew Brees said.

New Orleans (3-4) built its momentum Sunday on the back of a defense that might have found its calling card against an Indianapolis offense that looks like a shell of the unit Andrew Luck led to the playoffs the past three seasons.

Despite overall numbers that ranked near the bottom of the league, defensive coordinator Rob Ryan has remained adamant that his troops were on the verge of a breakthrough.

The Saints defense backed up Ryan’s words Sunday. Spearheaded by the attacking style of the defense’s emerging leader, defensive end Cam Jordan, the Saints forced three-and-outs on the Colts’ first two series, allowing New Orleans to capitalize on an aggressive call by head coach Sean Payton. With the Saints driving on their third series, Payton chose to fake a field goal instead of opting for three points, and Luke McCown hit Ben Watson for 25 yards to set up a Khiry Robinson 1-yard touchdown and a 7-0 lead.

“We felt like we were getting a pretty consistent look,” Payton said. “And I’m pretty bad about something like that. I can’t wait for the second. I’m pretty impatient.”

The New Orleans defense took the momentum and ran with it.

Rookie middle linebacker Stephone Anthony jumped a short route and picked off Luck on the next play from scrimmage. Five plays later, Robinson scored again, this time from 6 yards, and the Saints kept the heat on Indianapolis. David Hawthorne forced a fumble on the ensuing kickoff, and Brees responded by hitting Michael Hoomanawanui for a 16-yard touchdown pass that gave New Orleans a 20-0 lead.

Indianapolis simply couldn’t find its footing. By the time Kyle Wilson picked off a Luck pass in the red zone to end the half, the New Orleans defense had held the Colts scoreless and brought out boos from the crowd at Lucas Oil Stadium.

“It’s definitely a glimpse of what we can be,” Anthony said. “But we’d like to close games a little better.”

Luck has built his reputation on a history of comebacks, even early in his career.

And even after Mark Ingram scored from 1 yard to give the Saints a 27-0 lead midway through the third quarter, they had a feeling there was a charge coming.

“We know the character makeup of that team on the other side,” Brees said. “They have a ton of comeback victories. I’ve seen Andrew Luck do it a number of times. We knew the game was not even close to being over.”

True to form, Indianapolis came roaring back, in part by capitalizing on big New Orleans mistakes.

Brees tossed an interception in the end zone at the end of the first half, a moment when the Saints could have put Indianapolis away for good. Luck found T.Y. Hilton for touchdowns of 87 and 46 yards, scores made possible only because the Saints’ best cover corner, Delvin Breaux, tripped and fell.

And the Saints offense sputtered, able to flip the field with a couple of third-down plays, but unable to put any more points on the board. Despite continued inspired play from the defense, Luck brought the Colts within six points by hitting a wide-open Donte Moncrief for an 8-yard touchdown with 3:05 left.

New Orleans survived on the strength of Marcus Murphy’s recovered onside kick and a key third-down throw from Brees to Marques Colston, but the Saints know they should have put this one away much earlier.

“We have more in us,” Jordan said. “You can’t be too excited. We’re still 3-4. There’s some good things in the first half, but there’s some negative things that happened in the second half, and that’s something we have to get under control.”

From a larger perspective, though, this is a Saints team that has expanded its margin for error considerably. New Orleans was far from perfect Sunday; the Saints made their fair share of mistakes.

“We’re happy about winning on the road especially, but there’s lots of things we need to improve on,” Ingram said. “We need to finish better. We haven’t played a full game of our best football yet.”

Early in the season, that might have meant a loss.

But this Saints team is starting to learn how to win, even when everything doesn’t go according to plan.