The Phillies’ success in Game 3 didn’t come down entirely to one of their pitching aces, but more importantly to pinch hitter Ben Francisco’s three-run home run in the seventh inning of a 3-2 win in St. Louis. (SARAH CONARD/REUTERS)

The Phillies escaped October’s classic Game of Death here on Tuesday.

But how they did it, the maniacal capriciousness of their 3-2 win over the Cardinals in a pivotal Game 3 of their Division Series, was Exhibit A to explain why only three of the last 21 teams in the Phils’ shoes — owning the game’s best regular season record — have actually won the World Series.

The notion that any team, including Philadelphia and its Four Aces, is so good it can simply dominate postseason baseball without surviving constant cardiac calamities was exposed again Tuesday as a shibboleth, a canard and, well, you know, pretty much a barrel of stinking Mississippi catfish.

The Phils slipped the noose on a three-run seventh-inning homer by pinch hitter Ben Francisco after Tony La Russa, playing a hunch, intentionally walked No. 8 hitterCarlos Ruiz to get to him.

So the Phils’ winning run was an “intentional” gift of the Cards’ manager. Who also let his starting pitcher, a lefty who’d faced 26 hitters, pitch to Francisco, a right-handed hitter. Hook him? Nobody was hot in the pen.

The Phils also escaped because closer Ryan Madson got a five-out save, starting with an inning-ending double play that he induced from Allen Craig on a smash straight at second baseman Chase Utley. If it’s a yard to either side, it’s a two-run hit. And who was left on deck? Albert Pujols.

What did Pujols, the greatest hitter since Ted Williams, do on the first pitch of the next inning? Of course you know. He smoked his third double and fourth hit of the game. So, according to baseball-dugout thinking, that means, if Craig had simply struck out, Pujols would have come up with the sacks drunk in the eighth, cleaned them and St. Louis would’ve won, 4-3.

A logical fallacy? Bet you can’t find 10 players in this game who agree.

Of all the luck-soaked, nerve-shredding tests that drive baseball people nutty, the best (or worst) is this sort of five-game Division Series that, year after year, sets up some great regular season team to have its heart smashed.

And within that format, worthy of a torture chamber, the back-breaking fulcrum is Game 3 when it’s tied one game apiece. The winner has advanced to the League Championship Series 19 of 23 times. Those aren’t odds. That’s a near-death sentence if you lose.

“You felt like you were dodging bullets all day,” said Phils Manager Charlie Manuel who pulled as many right levers as La Russa yanked grenade pins.

“No, I wasn’t ‘nervous.’ Sort of excited, a little butterflies. That’s the fun of managing — you see games like this,” Manuel said. It’s a good thing he doesn’t get nervous, otherwise he’d look a thousand, not just 100.

This game also provided perhaps the 50th example, over many years, of a crucial game played at a ridiculous time to accommodate TV. The Cards and Phils played a game at a similar time earlier in the season that brought extended wails of protest that the ball simply could not be seen properly. This time, later in the year, the bad light didn’t last as long. But Garcia still got the first 15 outs on 51 pitches, 39 of them strikes. He pitched as if the Phils had no idea what was coming — even after they actually saw it. Which, of course, is exactly the case. You see a black spot, not a spinning baseball with seams that help the sharp-eyed identify the type of pitch.

Often, in a practical world, such 4 p.m. (local time) starting times are hard to avoid. This time, however, the Rays played the Rangers in St. Petersburg, Fla. — in a dome where there is no sunlight, no time of day — at 2 p.m. For a fraction of a ratings point, why not switch the Rays and Cards? At any rate, the net result was that nothing happened for almost six innings, 0-0.

The strategic crisis of this game was a dandy and provided an inning that, if the Cards are eliminated, will spoil many a winter night for La Russa, even though he broke no baseball laws. Sometimes, managing is like coming to a fork in a river and hearing rapids crashing in the distance. There’s no “right” decision. You weigh everything, including your gut. But, if you’re wrong, you still go over the falls.

With two on and two outs in the bottom of the sixth, La Russa let starter Jaime Garcia hit for himself. His pitch count was low. Maybe it wasn’t just the evil twilight, with the ball going from light to shadow to light to shadow in the early innings that had made Garcia so effective. Garcia fanned.

Having stuck with Garcia once, La Russa, the chest-out variety, wasn’t reversing course. With a man on second and two outs, he looked at Ruiz approaching the plate. “Ruiz terrorizes us. And he had already hit the ball hard twice. Garcia has had success with Francisco,” said LaRussa, adding, “But it didn’t work this time.”

Over the long season, and many years, the percentages will help you win. Ruiz was 1 for 5 in his career off Garcia while Francisco was 1 for 9. But is that enough difference, or a big enough data sample, to put an additional man on base, an additional potential run if you’re wrong? Better feel strongly, because in this case, it proved to be the eventual winning run.

La Russa’s opposite number, Manuel, is his opposite in every way. Charlie’s postgame analysis sounds like he attended a different game in another city. Until you parse it some more, then translate to Manuelese. Then it usually turns out he was ahead of you. And the guy in the other dugout, sometimes, too.

“Francisco can hit a fastball,” Manuel said. “I like him up there even if they brought in a right-hander. I definitely like him on a lefty.”

La Russa had the numbers. But Manuel “definitely” liked the matchup anyway. Garcia’s second pitch was a two-seam fastball up too high. Francisco drilled it 405 feet into the Cardinals’ bullpen in left field. Francisco thought he’d hit a double up the gap that skipped over the fence.

The ump told him he could slow down.

“Pure excitement,” said Francisco. “Pure joy.”

And for the Phillies, pure relief, too.

Now, their season can’t end here on Wednesday on the road before 46,914 red-clad Cardinal worshippers in what might also be a twilight start at 6:05 p.m. They know they get to go home for Game 5.

Most of all, they know how the odds and the momentum had changed. This time, the better team had dodged the Game of Death, the one that lies in wait, at least once, for almost every best-in-baseball regular season team.

Life may get easier for the Phillies now. But, since this is October, nah, probably not.