BOSTON — The grand slam is the most productive offensive play in baseball, the equivalent of a touchdown and two-point conversion in football, or a four-point play in basketball.

They are not exceedingly rare, but the Boston Red Sox managed only three of them in the 162-game regular season. Then came the American League Championship Series.

Over the last two games of the series — in a span of only 11 innings — the Red Sox hit three grand slams to establish a record for most bases-loaded homers in a postseason series. Kyle Schwarber did the honors in the second inning on Monday to propel Boston to a 12-3 victory over the Houston Astros in Game 3 of the A.L.C.S., Boston’s second straight runaway victory.

Behind another prodigious display of power, Boston has taken a two-games-to-one lead in the best-of-seven series and will host the next two games at Fenway Park, which are scheduled for Tuesday and Wednesday.

“Offensively, this is the best we’ve looked all season,” Red Sox Manager Alex Cora said, “and they’re locked in right now.”

Schwarber’s towering blast into the right field seats, off Houston starter Jose Urquidy, was part of a six-run second inning that turned a crisp, autumnal evening at Fenway into a massive party. More than 37,000 fans rollicked, swayed and yelled profane chants over the next three hours, secure that there was little chance the Astros would overcome such a deficit.

Boston added home runs by Christian Arroyo, J.D. Martinez and Rafael Devers as part of the 11-hit barrage and now have nine home runs in the first three games of the series.

Martinez and Devers hit the grand slams in the first and second innings of Game 2, so when Schwarber, Boston’s most productive hitter since joining the team in August, came to the plate with the bases loaded in the second inning on Monday, it was not a stretch to think he might do it again, especially after Urquidy fell behind, 3-0, in the count.

What made the situation even more dramatic was that the previous batter, Christian Arroyo, had hit a bouncer toward second base that could have ended the inning with a simple double play. But Jose Altuve, the Astros gifted shortstop, misplayed the high bounce and it deflected off him and into the outfield, allowing all the runners to advance safely.

The Red Sox fans hooted and shouted in delight and began to fantasize about a third grand slam in two games. Schwarber, however, was not indulging in those thoughts.

“I definitely wasn’t thinking home run, but I was definitely thinking, don’t be late,” he said, and added, “You know a heater is coming, and just go from there.”

The next pitch was indeed a fastball, and a juicy, fat one that bisected the home plate, belt high. Schwarber destroyed it, sending it several rows into the right field grandstand as the fans erupted. In the visitors’ dugout the reaction was more sober. Dusty Baker, the Houston manager, worried about a second consecutive game in which the starting pitcher faltered early on, and the implications for his overtaxed bullpen in the coming games.

“It’s kind of like Groundhog Day,” he said, “a recurring nightmare where you hope to get some innings out of these guys.”

For Cora, it was more of a dream come true. On his 46th birthday, he not only witnessed a definitive offensive outburst, he also saw several crisp defensive plays, including three by Devers at third base, and a fine outing by Eduardo Rodriguez, the left-handed starting pitcher, who had struggled in his first postseason start against the Tampa Bay Rays in their division series.

“Today was as close as we’ve been to a perfect game,” Cora said of the all-around effort.

Rodriguez struck out seven Monday, and allowed five hits and three runs, all of which came on Kyle Tucker’s three-run home run in the fourth inning that made the score, 9-3.

But when Rodriguez came off the field after his final out in the sixth, he made a gesture that had his manager scolding him from the dugout steps.

In Game 1, when Carlos Correa hit a go-ahead home run off Hansel Robles, he had stood at home plate, pointing to his wrist, asking rhetorically what time it was, then pounded his chest and yelled, “It’s my time.”

So, when Correa grounded out to end the sixth inning on Monday, Rodriguez pointed to his wrist as he walked off the mound. After yelling for Rodriguez not to do that, Cora met him at the steps of the dugout, wrapped an arm around his pitcher and gave him a stern message in his ear not to do things like that.

“Because we don’t act that way,” Cora explained later. “We just show up, we play and we move on, and he knows. I let him know. We don’t have to do that. If we’re looking for motivation outside of what were trying to accomplish, we’re in the wrong business. The only motivation we have is to win four games against them and move on to the next round.”

For the Astros to prevent that from happening will be difficult. They will send Zack Greinke to the mound to start Game 4 against Nick Pivetta, and they will hope it’s not another Groundhog Day.