The Rangers hold a season-high three-game lead in the American League West over the Mariners and have the best record in the American League (34-22) thanks to a season-best five-game winning streak.
"We obviously had to go in and make a statement against these guys," Holland said. "At the same time we're going to see them in less than five days. What we did was good, we just got to continue that now."
Holland has four consecutive quality starts since the rough outing at Toronto and is tied with Cole Hamels and Colby Lewis with a team-high five victories.
"I think Derek's fastball was fresh today, I think a difference maker for him," Rangers manager Jeff Banister said. "He had the [seven] punch-outs, four of which were the power fastball off the breaking ball."
The only blemish on Holland's line was a two-run homer off the bat of Nelson Cruz in the fourth inning that sailed an estimated 447 feet, per Statcast™. Other than that, he allowed just two singles and two walks.
"Holland threw the ball pretty good. We didn't have a ton of chances," Mariners manager Scott Servais said. "It was just one of those games you could kind of see we were going to need to win this one, 2-1, or, 3-2, or something like that."
Matt Bush and Jake Diekman combined to hold the lead in the eighth, before Sam Dyson came on in the ninth to pick up his seventh save and fifth consecutive since being named closer on May 18.
The Rangers have now won three consecutive series against American League West opponents since being swept by the A's on May 16-18. It was also their first series sweep of at least three games against the Mariners since August 2013.
"I think it's important [to get a sweep] any time during the season, especially when it's in division," Banister said. "… There's a lot of high energy there, a lot of confidence. This a heck of a ball club over there. This is a team that's going to be in the mix in this division all year long."
Ryan Posner is a reporter for MLB.com based in Arlington. This story was not subject to the approval of Major League Baseball or its clubs.