First they'll have to battle fatigue and finish a three-game set in Anaheim on Sunday after playing the longest game in the majors this season.
Los Angeles (68-48) ended a four-game slide with Saturday's 5-4 victory on Albert Pujols' leadoff homer in the 19th inning off Brandon Workman, the eighth Boston reliever used by manager John Farrell - who challenged the blast claiming there was fan interference to no avail.
It made a winner of Matt Shoemaker, who pitched three perfect innings of relief three days after he started against the Los Angeles Dodgers. He was the eighth pitcher used by the Angels after starter Garrett Richards, who no-hit the Red Sox (51-65) through six innings.
Dustin Pedroia broke up the no-hitter by leading off the seventh with a single and came around to score one of three runs for Boston in that inning, with two unearned thanks to two errors.
Mike Trout hit a tying homer in the eighth inning for the Angels and each team scored once in the 14th before Pujols finally ended a contest that lasted 6 hours, 31 minutes.
"It definitely gives us some momentum for tomorrow," Trout said. "It's going to be a quick turnaround."
It's hard to know which relievers will be off limits. Boston's Junichi Tazawa and Tommy Layne and Los Angeles' Jason Grilli and Fernando Salas have all pitched on four of the last five days for their teams.
These clubs will be able to rest their bullpens Monday with both off. But neither of Sunday's starters inspires much hope for doing so in this series finale.
Hector Santiago hasn't won in his last 17 home starts, including all eight with the Angels this year, while the Red Sox have dropped the last eight road games started by Rubby De La Rosa.
Santiago (3-7, 3.84 ERA) is 0-5 with a 4.20 ERA in his 17-start winless drought in home games. He is 0-3 with a 3.89 ERA in eight this year in Anaheim.
The left-hander went 0-2 with a 5.59 ERA in two starts last year against the Red Sox with the Chicago White Sox. Ortiz and Pedroia went 4 for 9 against him in those games while Yoenis Cespedes is 4 for 8 in his career with two homers versus Santiago.
De La Rosa (3-4, 3.43) is 0-5 with a 5.34 ERA in his road slide. His road ERA in five starts this year is 5.08 compared to 1.97 at home.
The right-hander's lone start against the Angels came when he gave up five runs over six innings in an 8-3 loss in 2011 for the Dodgers. He has never faced Pujols, Trout or Josh Hamilton.
Hamilton ended a streak of 23 at-bats without a hit with a double in the 17th inning Saturday but was stranded at third.
The Red Sox will give catcher Dan Butler his major league debut as De La Rosa's batterymate. Butler batted .227 at Triple-A Pawtucket.
"We think he is ready," Farrell told MLB's official website. "He has always shown in spring training and with Triple-A that he is more than capable of handling a big league staff and calling a big league game."