The Dodgers continued their season-long celebration of last year’s World Series triumph by handing out championship rings Monday. The 49,702 people who bought tickets got replicas while Gavin Lux, who played for the Dodgers last season and is now with the Cincinnati Reds, got a real one.

If the team hopes to win more jewelry again this fall, the next five weeks will be key. Because after Monday’s 7-0 win over the Reds, the Dodgers lead San Diego by a game in the National League West with just 30 more left in the regular season for both teams.

However, if the Dodgers (75-57) continue to play as they did Monday, when Andy Pages homered twice, driving in four runs, and Emmet Sheehan threw a career-high seven scoreless innings, they’ll be tough to catch.

“The defense was just engaged, every single guy out there. The at-bats, one through nine, were great,” Dodgers manager Dave Roberts said. “It’s probably one of the better games, complete games, that we’ve played in months. I’m really, really excited about the way we played.”

Excited, too, because what started as a marathon six months ago is now a different kind of race.

“We’re in a sprint now,” said Michael Conforto, who had two hits and made two outstanding plays in left field. “We’re in a race for the division.”

And they’re a step ahead in that race with the Padres, who, like the Dodgers, have 10 series remaining, five at home and five on the road. But San Diego has the easier schedule, based on the combined winning percentage of its opponents (.474) entering the week. The Dodgers have the fourth-easiest schedule.

For Roberts, his team’s narrow margin for error is something to be embraced since it has the potential to steel his team for the postseason, as opposed to simply coasting into the playoffs.

“Competition should bring out the best in you,” he said. “So where the margins are smaller and everything matters more versus you have a big lead and you’re not playing with urgency because you don’t need to, and then have to kind of flip the switch, that’s tough.”

The Dodgers also are rapidly adding reinforcements for their playoff push. Over the weekend, relievers Tanner Scott and Kirby Yates returned from the injured list and utility player Kiké Hernández was activated Monday. Third baseman Max Muncy and infielder/outfielder Hyeseong Kim could be back by the next road trip, if not before. Utilityman Tommy Edman and pitcher Roki Sasaki likely aren’t far behind.

Then there’s Sheehan (5-2), who was brilliant Monday, pitching a career-best seven innings and matching a career high with 10 strikeouts to win his third straight decision. Sheehan gave up just two hits and walked one.

“I definitely have to build on it. Try to just keep the same progress we’ve been doing, keep that going for the next one,” Sheehan said. “It’s pretty fun. It’s a lot more fun than watching the ball go over the fence, for sure.”

For Roberts, it’s as if his team acquired a half-dozen new players.

Dodgers shortstop Mookie Betts, left, celebrates with right fielder Teoscar Hernández after hitting a home run in the seventh inning against the Reds on Monday.

(Carlin Stiehl / Los Angeles Times)

“Those are kind of deadline trades in themselves,” he said. “I do appreciate the guys that have been here, kind of grinding through. But it’s nice looking out on the horizon, seeing the guys that we got coming.”

Pages put the Dodgers in front to stay in the third Monday, driving a 102-mph fastball from Hunter Greene into the bullpen in left field. He hit another in the fifth inning for his 23rd homer of the season, second-most on the team behind Shohei Ohtani’s 45.

In the sixth, a double by Freddie Freeman and walks to Will Smith and Teoscar Hernández loaded the bases for Pages, whose two-out grounder to short got under Elly De La Cruz for a two-run error. A Mookie Betts’ homer, his second hit of the game, with one out in the seventh and a Pages’ sacrifice fly in the eighth closed out the scoring.

Relievers Jack Dreyer and Anthony Banda followed Sheehan, pitching an inning each to complete the shutout, the team’s fourth in the last 23 games.

The Dodgers had only three shutouts in the first 109 games.

Now come the reinforcements, although Kiké Hernández said he almost didn’t make it. After going on the injured list July 6 with left elbow inflammation, he tried three injections and non-invasive rehab procedures, but nothing seemed to work.

“I got to a point where I didn’t know if it was going to happen. We were pretty close to it not happening,” he said of his return. “There are some procedures that I went through that didn’t do anything. I went through four shots in a month, and [the] first three didn’t do anything, and luckily the fourth one was the answer.

“After the last shot, I was pain free.”

Hernández said he expected to start in left field Tuesday. He joins the Dodgers just in time for their sprint to the finish.

“It’s playoff-atmosphere games from here on out,” he said. “Hopefully it brings out the best in people and also teaches the younger guys that when the time comes and we’re in October, the moment doesn’t get too big for them.”