BOSTON -- A strong start from Eduardo Rodriguez. Another early grand slam -- this one by Kyle Schwarber. A perfect 46th birthday for manager Alex Cora, who is watching with passion as everything is suddenly going right for his surging Red Sox.

That familiar October feeling is back at Fenway Park, where the home team is 4-0 this postseason.

This, after the Red Sox hammered the Astros, 12-3, in Game 3 of the American League Championship Series before a revved-up home crowd of 37,603 on Monday night.

• 7 amazing stats from Boston's Game 3 romp

"Today was as close as we've been to a perfect game, to be honest with you," said Cora. "We pitched well, played great defense, we ran the bases. We were very aggressive in a lot of aspects, so tonight is one of those that you feel good about."

Boston, which played the underdog role well in a 92-win regular season and again in this postseason (the Rays and Astros were both favored to beat Cora's club), is now just two wins away from the World Series.

If the Red Sox have it their way, they will finish this ALCS off at home by winning the next two days. In all best-of-seven postseason series tied 1-1, the Game 3 winner has gone on to win the series 66 of 95 times (69%).

"I think we play one game every day," said catcher Christian Vázquez, who chipped in with a couple of big hits. "We don't get ahead of ourselves, but we go out there and give everything we got to try to win every game we play. The first game we almost had them, but it's part of the game. Turn the page and get the second game and third game. And we're now in a good place."

Offensively, they're in a place a lot better than good. They look overpowering.

"Offensively, this is the best we've been the whole season, and they're locked in right now," Cora said.

Meanwhile, the heavy-hitting Astros have been outslugged and outpitched by the Red Sox in a big way over these last two games. Houston's 5-4 win in Game 1 now feels like a long time ago.

However, momentum can turn quickly this time of year and the Red Sox will try to make sure that doesn't happen.

"We'll be ready for tomorrow," Cora said. "That's a really good team out there. It's never comfortable with them. We got to be ready."

Speaking of ready, it was Rodriguez who set the tone in Game 3 by coming out of the gate with three scoreless innings. The Astros haven't had a starter go as many as three innings in this series.

While E-Rod went six strong innings (five hits, three runs, no walks, seven strikeouts), Astros righty José Urquidy was lifted with two outs in what snowballed into a six-run second inning for the surging Sox.

The biggest swing came off the bat of Schwarber, who unloaded for Boston's third slam of the series -- and in the last two games. The Red Sox are the first team in postseason history to have three grand slams in one series.

Schwarber gripped and ripped for the first homer of his career on a 3-0 count. Including the postseason, Schwarber came in 1-for-8 in his career when he put the ball in play on a 3-0 count.

That 430-foot moonshot to right, which boomed off the lefty slugger's bat at 114 mph, put Fenway into a frenzy, and it stayed that way for most of the night.

• Papi's must-see reaction to Schwarber's slam

"That gave me a headache, and I loved it," Schwarber said of the deafening roars as he rounded the bases. "I loved every second of it. Like I said, this is what you live for, right? This is it."

Christian Arroyo, not too worn out from singing and dancing at the Patriots-Cowboys game on Sunday, added a two-run shot in the third. It was Arroyo's first career postseason homer, and one he won't soon forget.

"It's truly special," Arroyo said. "It's just one of those moments you're never going to forget, and you kind of are on this platform where you don't really know what to do. You kind of black out for a second."

J.D. Martinez unloaded for a two-run shot of his own in the sixth and the rout was on. Rafael Devers capped Boston's scoring with a solo dinger into the Monster Seats in the eighth.

The Red Sox are obliterating the baseball in this series -- and throughout this October -- like the Astros expected to. Boston's 20 homers this postseason ties it with the 2004 Houston club for the most by a team through the first eight games of a playoff run.

"I mean, they count as one," said Astros manager Dusty Baker. "We come back and win tomorrow, the series is even. You don't like it. I'm not very happy about it, but you got to flush this one, because you can't bring this one or the last one back until tomorrow. And so, like I said, you don't like it tonight, but the sun is going to come up in the morning."