"Finishing fourth, fifth -- if you're not finishing first or going to the playoffs, it's not a good season," manager Dale Sveum said.
Lake is having a good season. He now has 55 hits in his first 45 games, tops among Major League rookies in that stretch.
Gregg pitched the ninth for his 30th save, marking the third time he's reached that mark. The veteran, who was released by the Dodgers this spring and didn't sign with the Cubs until mid-April, has now saved half the Cubs' wins.
"It's one of those benchmarks for a closer," Gregg said of reaching 30. "From the way my year started, it's pretty exciting to get to.
"Being released out of Spring Training and not having a job for the first two weeks of the season, it was a pleasant surprise to come in here. I had to work for it, and I earned the role. I ended up with 30 saves -- so far."
"Who would have thought that when we left Spring Training that Kevin Gregg would be getting 30 of our saves?" Sveum said. "He's done one heck of a job. It'd be tough to imagine what we would have done without him."
Before the Cubs got to Gregg, they scored five runs in the first against Milwaukee starter Kyle Lohse. With one out, three batters singled, with a run scoring on Nate Schierholtz's hit. Ryan Sweeney then walked to load the bases, and one out later, Lake drove a 1-0 pitch into the bleachers in left-center. It was his fifth home run of the season and the Cubs' third grand slam this year.
"[The slider to Lake] just spun right there," Lohse said. "The frustrating thing was, I felt like, first and third, I was one pitch away a couple of times, and I just didn't make the pitch. It happens. It was frustrating, but it's going to happen from time to time, and unfortunately, it cost us the game early."
The Brewers scored in the second on Norichika Aoki's sacrifice fly. Aramis Ramirez, who played for the Cubs from 2003-11, hit his 127th home run at Wrigley, and 10th this year, with one out in the third to close to gap to three runs.
Lake showed his maturity in the Chicago third. Sweeney and Donnie Murphy singled, and Lake then bunted for a base hit to load the bases and set up Rusin, who delivered a two-run single and opened a five-run lead. Cubs pitchers now have 27 RBIs, the most in the Majors.
Lake could have swung for the bleachers again but didn't.
"It's hard to go up there after hitting a grand slam and not think about two homers and seven [RBIs] in your pocket," Sveum said. "It led to bases loaded and nobody out, and we ended up getting two out of it. It's nice to see a guy thinking about other things than his own stats."
"I know I can hit another home run," Lake said, "but it's not about me, it's about the team. I think it helps the team if I bunt for a base hit or make a sac bunt."
Rusin needed 32 pitches to get through the first and was pulled after throwing 85 over 3 2/3 innings, giving up two runs on seven hits.
"I guess that kind of salvages the day," Rusin said of his two RBIs. "I felt I was nibbling, and good hitters like they are, they'll take those pitches. You have to be able to attack the zone with other offspeed [pitches] on different sides of the plate, and I was struggling with my offspeed and trying to work with what I had."
Carlos Villanueva picked up the win after throwing 2 1/3 innings in relief, his third win in his last four appearances.
"I'm just going to pitch him in any situation where he has a chance to win now," Sveum said of Villanueva, who struck out five of the seven batters he faced.
Milwaukee made it interesting in the eighth when Scooter Gennett delivered his first career pinch-hit home run, a three-run shot, to pull the Brewers within two. In the Chicago half, Murphy scored from third on a throwing error by shortstop Jean Segura.
Gregg finished the game with a 1-2-3 ninth and has reached 30 saves for the first time since 2010, when he finished with 37 for the Blue Jays. The right-hander, who will be a free agent when the season ends, still has something left.
"I hope so," Gregg said. "That's the idea."