BALTIMORE -- The Rangers did their part to help the Orioles continue their journey toward the worst record in the American League. Now they get ready for their own final 17 games against teams fighting for the postseason.

The Rangers, riding a 20-hit attack and the solid pitching of starter Mike Minor, completed a four-game sweep of the Orioles with a 10-4 victory on Sunday afternoon at Camden Yards. This was the Rangers' first four-game sweep of the Orioles in Baltimore since July 7-9, 1972. (That series included a doubleheader.) In an interesting wrinkle, the Rangers finished 54-100 that season, while the Orioles were coming off three straight American League pennants.

Texas, which is now just one game under .500, has six games to play against the Athletics, three each against the Rays, Red Sox and Yankees and two against the Astros. The team with the best overall record gains home-field advantage through the World Series, so the Yankees and Astros will have something to play for, even though they are both running away with their divisions.

• Box score

“This is a great challenge,” outfielder Delino DeShields said. “There are a lot of kids up here for the first time in the big leagues and this is really going to tell where they are as far as competition. We are going to go out and try to win every single game. We want to ruin people’s chances if we can, or hold them off as long as possible and finish the season on a high note.”

The Rangers begin the stretch with a three-game series against the Rays on Tuesday night at Globe Life Park and are a combined 15-25 this season against their five remaining opponents. But the Rangers have plenty to play for as well.

“We are in a situation where only a few guys on our team have a solidified position next year,” Rangers manager Chris Woodward said. “That’s just speaking the truth. Guys are still fighting for their jobs and fighting to show us their role for next year. That helps us, because guys aren’t going to take anything for granted.

“We are trying to build on something to be good, to be great, either next year or the year after, and it’s important. Every game is important, especially with tough teams coming up. I don’t want to go into the offseason thinking we just limped our way to the finish line. Let’s run through the finish line.”

The Rangers, at 72-73, have already won five more games than last season (67-95). While they face a tough finishing schedule, a winning record is still within their grasp.

“Weren’t we supposed to be a 60-something-win team?” Minor said. “Everybody has seen how we improved on that. It’s going to be difficult, but I think we can still get some wins and some series wins against these guys and maybe knock [some of] them out. It might come down to one game for them and that one game could be a loss against us. It’s a little bit of a motivation.”

Minor has some personal motivation as well. He earned his 13th win by holding the Orioles to two runs over eight innings. That ties his career high in wins (2013 with the Braves), with three starts to come. He is also at 189 2/3 innings and 183 strikeouts on the season. He would like to get to 200 in both categories.

“I think it’s better for us to play good teams like that,” Minor said. “Guys play up [to the competition]. We know those teams are coming in and trying to sweep us, try to get as many wins as they can because they are trying to make the playoffs and we aren’t. But we are still trying to kick somebody’s rear. I think everybody will be ready when they come in.”

Woodward said the Rangers had their best approach at the plate in a long time on Sunday, and the results showed. The 20 hits were tied for their second-most in a game this season, and everyone in the starting lineup had at least one hit by the end of the fourth inning.

Rangers designated hitter Nick Solak, batting in the cleanup spot, and catcher Jose Trevino, at the bottom of the lineup, both had big afternoons. Solak was 3-for-4 with a run scored and four RBIs while Trevino was 3-for-4 with a run scored and a sacrifice fly. Ronald Guzmán and Shin-Soo Choo both had three-hit afternoons, and Rougned Odor hit his 24th home run.

“In baseball, you never know what will happen,” Choo said. “Every game from now on will be against a top team but we don’t have to do anything different, just keep doing what we did in the last four games.”