There’s too much history — quirky, gut-wrenching, heartbreaking chronicles passed from generation to generation — for Red Sox Nation to get cocky now.

No premature orders of champagne. No crazy celebrations. Nothing that would risk jinxing a team that has lived with a jinx since 1918.

Yet a thrill is in the air, as surely as the autumn coolness. Smiles are as vivid as the brilliantly colored foliage. There is a lightness in fans’ steps, fewer wrinkles in their brows. The natural inclination of New Englanders toward pragmatism, even pessimism, is being stripped away by an irrepressible giddiness. It feels so beautifully unfamiliar.

The Boston Red Sox are halfway to capturing the World Series, up two games to none against the St. Louis Cardinals after Sunday night’s 6-2 victory, and riding a six-game postseason winning streak.

They are winning despite more misadventures in the field. But what’s another four errors when a team has an inspirational leader like Curt Schilling on the mound? There he was, deliberate as ever, blowing on his fingers between pitches, zeroing in on the corners of the plate, playing with his ankle bleeding again and his hip flexor so sore he needed a hot water bottle between innings in the dugout.

What do a few mistakes matter when the whole lineup is clicking, everyone reaching base with hits or walks, doubles and triples?

The Red Sox know they can’t take anything for granted right now, not when they’re going to St. Louis, losing the designated hitter for the next three games — if there are three — and playing on a field where the Cardinals are 6-0 in the postseason.

“We are not going to fall into the trap after winning the first two,” Boston’s Alan Embree said. “You saw what happened with the Yankees. They’ve got a great ballclub over in that clubhouse, one that is just like ours.”

The Cards surely are no pushovers. They led the majors in wins in the regular season, have a lineup every bit as potent as the Red Sox’s, and fans every bit as passionate.

“We like playing on the road. We love playing at home. So, like versus love,” St. Louis manager Tony La Russa said. “Our fans are going to be crazy and look to give us a boost. But we are disappointed we didn’t get a game here or more.”

If the Cards are flat at the moment — batting .239 in the first two games, compared with the Red Sox’s .304 — they can turn it around in any inning.

They face a tough pitcher in Boston’s Pedro Martinez but there’s no reason to think that the Cards can’t beat him, even if they could muster only five hits against Schilling and the three relievers who succeeded him.

That doesn’t mean there’s any sagging of the Red Sox’ confidence.

“I expect Pedro to pitch his fanny off,” Boston manager Terry Francona said. “I think he’s got rest. I think he feels good about himself. We’ll have a day off, so we can rest our bullpen a little bit. Anytime we start Pedro, believe me, we’re excited about it.”

This cool, damp, misty night, though, belonged to Boston, to the players who are self- proclaimed “idiots” who don’t care about history, and to the fans who held so many signs that read, “Believe.”

It belonged to Jason Varitek, calling the game for Schilling behind the plate and hustling on heavy, tired legs around the bases on a rare triple — a two-run shot off the base of the wall in center that runs, oddly, perpendicular to the 420-foot sign nearby.

It belonged to Bill Mueller, who doubled in a run, scored another, singled and walked, giving Boston a boost in the eighth spot.

It belonged, most of all to Schilling, who woke up in the morning unsure if he would be able to pitch.

“I promise you that when I walked out of that dugout today and headed to the bullpen, the most shocked person in this stadium was my wife because I woke up at 7 o’clock this morning, which is a tip-off right there,” Schilling said. “I’ve never woken up at 7 in the morning for anything in my life.

“I wasn’t going to pitch. I couldn’t walk. I couldn’t move.”

He didn’t know what had happened. He had his ankle stitched up Saturday as it was Monday, sutures from his skin to the deep tissue below near the bone keeping his dislocated tendon from flopping around. But now it hurt badly.

“I wasn’t going to go out on the mound with the way I felt today,” he said. “There’s no way. And that’s kind of when everything just started.”

He got in his car at home in Medfield and looked around with astonishment.

“There were signs every mile from my house to this ballpark, on fire stations, on telephone poles, wishing me luck,” he said.

He had to find a way to pitch, and the doctors found it for him. The one extra stitch that was put in this time, four instead of three, was removed, he got a shot of a numbing medication, and suddenly Schilling felt better. He could stand without pain, walk without pain, and he knew immediately he could pitch without pain.

He credited his faith and the fans.

“They believe in me to the umpth degree,” he said. “A lot of times I tell the other guys, ‘Don’t be the only guy not believing in yourself. Everybody here believes in you.’ That’s what I tried to walk out there with tonight.”

Red Sox Nation isn’t breaking out the champagne yet but, after watching Schilling, it believes more than ever that its time may finally have come.