CHICAGO — As the Saints prepared to visit the Bears at Soldier Field, where they’d lost the three times they played there in December or January under coach Sean Payton, most of the players in the locker room were reluctant to talk about the importance of the showdown.

Most said it was the biggest game of the season solely because it was the next one on the schedule. Others talked about how it felt like a regular work week.

But the reality of the situation was that the Saints would’ve lost control of their playoff destiny if they had been defeated by the Bears on Monday night — they would’ve needed to win their last two games and for divisional foe Carolina (5-8-1) to drop one of their final pair.

However, one player didn’t mind acknowledging the magnitude of the contest: franchise quarterback Drew Brees, who in no uncertain terms said, “We are playing for a tremendous amount. We couldn’t be playing for more.”

And, boy, did he play like it in the Saints’ 31-15 win over the Bears (5-9).

The Saints (6-8) opened up a 14-0 lead at the end of the second quarter that the Bears simply had no chance of reverting because Brees played perhaps his best half this season. He completed all but two of the 20 throws he attempted — 90 percent — in the first half for 226 yards and a pair of touchdowns, giving him a world-class passer rating of 147.1.

Compare Brees’ halftime passer rating to that of his counterpart, a struggling Jay Cutler (14.9), and appreciate why it is that Bears fans packing Soldier Field’s stands booed bitterly at various junctures Monday.

Brees finished 29-of-36 for 375 yards, three touchdowns and a passer rating of 137.8, his third highest of the year. He did not register any of his scoring throws with his starting left tackle, Terron Armstead, protecting his blind side.

“I saw a lot of ... guys just ready to play and ... cut it loose — not playing with any inhibitions or caution or paralysis by over-analysis, just going out there and playing ball and doing like we know how we need to do,” Brees said of Monday night.

Armstead reaggravated a neck injury that had his playing status against the Bears in question and went down on New Orleans’ third offensive drive, when the game was scoreless. He was replaced by backup Bryce Harris.

Brees, who was sacked two times in the game, responded to losing Armstead with an 8-yard, play-action touchdown pass to second-year tight end Josh Hill and a 9-yard TD strike to veteran Marques Colston, each in the second quarter. The scores came at the end of a seven-play, 85-yard drive and a 10-play, 95-yarder, and Colston’s left the Bears with 32 seconds to answer before halftime.

The Bears didn’t and kicked off to begin the third quarter. The Saints immediately went 80 yards in 12 plays, and Brees finished the drive with a second TD to Hill, the young tight end’s fifth of the campaign. This one was from 7 yards out, the Saints’ third touchdown from inside the Bears’ 10, which hints at how efficiently New Orleans moved the ball on a Chicago defense that admittedly was vulnerable, ranked 29th in the NFL in total yards. Up 21-0 with 8:35 in the third quarter, the game was essentially over.

New Orleans could’ve been up more at that point. But, on the Saints’ second offensive snap, after an interception, third-year receiver Nick Toon lost a fumble after catching a pass at Chicago’s 5. Then, after driving to Chicago’s 33, kicker Shayne Graham slipped on a 51-yard field goal try and missed short.

In the second quarter, after reaching Chicago’s 26, Harris surrendered a sack of Brees to Chicago’s Willie Young. That pushed the Saints out of field goal range, and they punted.

Those amounted to blown opportunities that could’ve widened the Saints’ advantage over the Bears, who also gave up a field goal to Graham as well as a scoring run by Mark Ingram (his career-high seventh of the year).

“(Those were) a couple of squandered opportunities,” Brees said. “We’d like to see seven points there.”

Yet, while the Saints’ performance wasn’t perfect, they’ll welcome it after losing in New Orleans to Carolina eight days earlier by 31 points.

“We were embarrassed about what happened last week,” Brees said. “We know we were better than that, and certainly a great sense of urgency just knowing what’s at stake and what a win would do for us not only from the standings but from a confidence standpoint.”

They’ll welcome it, as it produced a third straight away victory for the Saints to soften the effect of a four-game home losing streak on which they’ll enter their contest in New Orleans on Dec. 21 against the archrival Atlanta Falcons (5-9).

And all of that will at least temporarily silence those who have been questioning Brees’ longevity in New Orleans in part because he’s thrown 12 interceptions this season, none of which were on Monday night.

Brees said it was important to demonstrate in Chicago they could rebound from the thrashing they took from Carolina. But now the priority is to not ease up the intensity with Atlanta less than a week away.

“Learning how to handle success is as important or more important than handling adversity,” Brees said. “The tendency after success is to relax, and it’s not time to relax — it’s time to hit the pedal to the medal and continue to get better.”