OAKLAND -- It's never great to start your day by giving up a leadoff double. Especially not when it's followed by another two-bagger a couple of batters later, losing the slim lead your team just earned.

Rich Hill wasn't too bothered. He struck out his next batter to end the inning. And then he hit a groove, retiring 16 straight A's batters.

Sunday’s outing was just what Hill needed after a three-game stretch in which he went 0-2 with a 9.82 ERA -- including his worst start of the season last Monday in Baltimore, where he gave up six earned runs in four innings of work.

It was also exactly what the Red Sox needed to top the A's, 5-2, securing the series sweep and at long last returning to a .500 record on the season. Boston hasn't been at .500 since April 22, when the team reached 7-7 after a 4-3 win at Tampa Bay, and was as many as nine games under .500 as recently as May 11.

"We know we have a good baseball team that has to keep working hard to accomplish what we want, and we've been playing good baseball the last three weeks, just grinding and using everybody," manager Alex Cora said. "We've still got holes, but … we feel very good about ourselves trying to win on a nightly basis."

Said Hill: "Everybody's clicking -- starting pitching, infielders, outfielders. The hitting is coming around, and the bullpen's been doing a great job, so just continue to keep pushing forward, and tomorrow's another day."

The game had all the makings of a pitchers' duel after both Hill and A's starter Frankie Montas surrendered runs in the first inning. They traded zeros until the sixth inning, when right fielder Franchy Cordero broke the game open with a three-run blast to left.

It was Cordero's third homer of the year -- his second go-ahead shot -- and he said he was happy to be able to help lift Hill to a win during his strong outing.

"That's the main goal for me," Cordero said, "just try to help the team win, and try to get good at-bats and try to do my part."

Hill went six innings, tying a season high, and even pitched to one batter in the seventh -- though he gave up a leadoff single to Oakland's Jed Lowrie, ending his retired-batters streak and his afternoon.

So, what did Hill do differently on Sunday afternoon? His stuff wasn't overpowering, only getting six whiffs -- just two more than teammate John Schreiber got in only one inning of work. He's not a flame-thrower either -- his four-seamer topped out at just under 90 mph, and his average velocity was 78.1 mph on the afternoon.

"Good fastball command, we mixed up a few cutters, too," Cora said. "The breaking ball played, he had them off-balance, but I think it starts with fastballs, and he did an amazing job."

One key to Hill's success on Sunday was his cutter. Hill threw it nine times, seven for strikes. He doesn't use the pitch very often -- so far, he has thrown it less than 1% of the time this season -- but he joked postgame that it had been "here and there the last 20 years."

Hill, 42, has made several stops during his 18-year Major League career, and one of those places was Oakland. He started 14 games for the A's in 2016, pitching to a 2.25 ERA before his eventual trade to the Dodgers.

And whom did the A's receive for Hill? Three Minor League pitchers, one of whom was his opponent on Sunday, Montas.

When Hill left the game in the seventh inning, he received an ovation from the fans in the Coliseum seats. Whether it was led by the sea of visiting fans in red or the hometowners who remember him from his Oakland days, Hill had one word to describe the gesture.

"Special," Hill said. "I don't take any of these moments for granted, because you don't know how many more of them you have, so you want to continue to enjoy the game as much as possible. The support is definitely appreciated by everybody in the clubhouse."