Texas Manager Ron Washington pushes the play button

One has a law degree, speaks multiple languages and approaches a baseball game with all the joy of a root canal.

The other is homespun, wise-cracking and animated, a baseball lifer who shows up at the ballpark every day looking as if he just won the lottery.

Yet with the World Series heading back to St. Louis for Game 6 on Wednesday, there’s just one game separating Tony La Russa’s Cardinals and Ron Washington’s Texas Rangers, with Washington and the Rangers holding a 3-2 lead in the best-of-seven playoff after a 4-2 victory Monday in Arlington.

If there’s little separating the teams on the field, though, there’s a huge contrast in the styles of the men who run them. And some of that contributed to Monday’s win.

La Russa is widely considered baseball’s greatest tactician, a master manipulator of lineups and the double-switch. But he tends to attack a game like the Wehrmacht did Poland.

Washington, while far from a slouch when it comes to the Xs and O’s, is a master motivator, a guy who prefers a bear hug and a smile to a kick in the pants. He tends to attack a game like a kid attacks Christmas morning.

“It’s true, it’s pure, it’s not a show,” Nolan Ryan, the Rangers president and chief executive, said of Washington’s exuberance. “That’s just him and his personality.”

And at a time when most games — especially championship games — take on an importance far beyond what they deserve, Washington’s playfulness is like a cool breeze on a hot Texas day.

“He cares about his players,” said Rangers left-hander Derek Holland, who got a fatherly talk and hug from Washington before shutting down St. Louis in Game 4. “He is a very motivational coach … and he shows that he cares about every single one of our players.”

The two managers matched wits Monday mostly by purposely putting guys on base.

In the third and fifth innings, Washington walked the Cardinals’ Albert Pujols intentionally with runners in scoring position and first base open. The move worked both times.

La Russa tried that strategy once, in the eighth when he put Texas’ Nelson Cruz on base with one out, then waved in left-hander Marc Rzepczynski, who gave up an infield single followed by Mike Napoli’s game-winning two-run double.

Afterward, La Russa, who stands sternly in the corner of the dugout, sternly staring at the field like Bill Belichick on the Patriots’ sideline, said he had the wrong pitcher on the mound. He wanted hard-throwing right-hander Jason Motte to face Napoli. But when he called to the bullpen, coach Derek Lilliquist misunderstood him and had Lance Lynn warm up instead.

“I saw Lynn, I went, ‘Oh, what are you doing here?’” said the master strategist.

So La Russa let the wrong pitcher throw to the wrong guy with the bases loaded in a tie game in the World Series?

Washington, meanwhile, pressed all the right buttons. Aside from ordering four intentional walks — none of which led to a run — Washington called on a conga line of relievers who helped strand 12 Cardinals runners on base and limit St. Louis to one hit in 12 at-bats with runners in scoring position.

“I’m not as dumb as people think I am,” Washington said. “They call it unorthodox, I just call it reacting to what the game asks you to do. I’ve got personnel that can do a lot of things. And sometimes those things make us look like we’re renegades.

“But we’re not renegades. We can play baseball.”

And even their manager appears to be having a lot of fun doing it.

kevin.baxter@latimes.com