Texas scored at least 10 runs each time.
The Rangers will look to keep the bats moving and seek to win for the sixth time in seven games overall when they host the Mariners on Tuesday in the middle contest of a three-game series.
The Rangers also had five doubles, and all 10 of their runs were necessary as the Mariners scored seven runs over their final two at-bats before falling for the 16th time in the past 21 games.
"You have to play all nine innings," Pence told Fox Sports Southwest in a postgame television interview. "You have to keep going and keep adding on. They're a great offense, too, and they've been swinging it well.
"Every run, every at-bat is important, and we have to have good at-bats. We keep preaching that."
Earlier this season, the Rangers posted wins of 15-1 and 14-1 on consecutive days in Seattle. Texas is averaging 13 runs in its three victories against the Mariners this season.
Seattle pitching has allowed at least 10 runs in three of its past five games overall and 11 times this season.
Allowing five runs in the first inning of the opener dug a hole that the Mariners couldn't escape.
"Our guys didn't quit offensively," Seattle manager Scott Servais said during his postgame press conference. "In this ballpark, the way the wind is blowing, the ball is going to get out of here in a hurry.
"Offensively, our guys kept swinging the bats. We will get back at them (Tuesday). There is going to be a lot of runs scored in this series."
Cabrera certainly is enjoying playing at Globe Life Park. All nine of his homers and 24 of his 25 RBIs have come at home.
Seattle's Tim Beckham Jr. hit his first career grand slam on Monday while going 3-for-4 with a career-best five RBIs. He was 7-for-41 (.171) with two solo homers in May before breaking out in the opener.
"That was good to see," Servais said. "He was so hot early in the season. It was nice to see his bat get warmed up again."
Seattle will recall journeyman Tommy Milone on Tuesday to make the start against the Rangers.
The 32-year-old left-hander was signed to a minor league deal in the offseason, and he went 4-2 with a 3.83 ERA in nine games (eight starts) for Triple-A Tacoma.
Milone is 46-37 with a 4.42 ERA over 151 appearances (130 starts) in parts of eight big league seasons. He notched 25 of his victories during a two-year span with the Oakland Athletics (2012-13) and has just five wins over the past three seasons with the Minnesota Twins, Milwaukee Brewers, New York Mets and Washington Nationals.
"For me it's a matter of getting back to being consistent on a game-to-game basis," Milone told reporters. "For a few years, I just wasn't consistent. That's the biggest thing is going out and have the team rely on you that you can get the job done, and I'm feeling good about that right now."
Milone is 3-4 with a 4.53 ERA in 10 career starts vs. the Rangers.
Right-hander Lance Lynn (5-3, 4.94 ERA) will take the mound for Texas, and he is looking for his sixth win in the past eight starts.
Lynn defeated the Kansas City Royals in his last turn on Thursday when he gave up one run and six hits over seven innings.
Lynn beat the Mariners during the stretch. He matched his season best of nine strikeouts on April 28 when gave up one run and five hits over seven innings of a 14-1 victory.
Lynn is 2-0 with a 2.08 ERA in two career outings against Seattle.
Seattle's Ryon Healy exited the Monday game due to a back strain. His status will be determined Tuesday.
--Field Level Media