Morse had four hits, including the go-ahead homer in the eighth inning after Washington had blown a four-run lead, and the Nationals beat the Atlanta Braves 5-4 on Friday night.
More, who missed the first 50 games with a back injury, has four straight multihit games and is 13 for 23 in a five-game hitting streak.
"I'm starting to have better at-bats, starting to recognize pitches and see pitches," said Morse, who raised his batting average from .265 to .294.
Morse was under instructions to let manager Davey Johnson know if he had more tightness in his right hamstring, a problem that emerged this week in Colorado. Morse let Johnson know in the seventh inning "it was tightening up a little bit."
Morse's home run in the eighth allowed him to protect the hamstring as he casually jogged around the bases.
"I told him his swing kept him from running," Johnson said with a smile.
The homer was only the third for Morse but it was his second in two days. Morse, who hit 31 homers in his breakout season with Washington in 2011, hit a three-run homer at Colorado on Thursday.
"He's been looking better and better every day," Johnson said. "It's nice to have him back. ... We'll probably move him back into the cleanup spot."
Morse had a quick answer by hitting right-hander Chad Durbin's first pitch over the wall in right field leading off the eighth.
"He's got a lot of juice going that way," Durbin said. "We come back, score four, it would have been nice to keep it even."
The Nationals, who swept a three-game series in Atlanta on May 25-27, are 5-1 against the Braves this season. First-place Washington is 4 1/2 games ahead of Atlanta. The Nationals began the night 3 1/2 games ahead of the Mets.
"You want the games like this, because you want the emotional games," Simmons said. "You want to battle and win. It makes you feel good. It makes you feel like you accomplished something. But after battling that much and losing, it hurts."
Detwiler allowed only two hits through six scoreless innings, but he couldn't hold the 4-0 lead in the seventh.
Detwiler hit Freeman with a pitch and then bobbled a bunt by Jack Wilson, who was awarded an infield hit. A balk by Detwiler moved the runners to second and third.
Pinch-hitter Prado's single drove in Freeman. Bourn's fly ball scored Wilson, and Simmons followed with his tying two-run homer, knocking Detwiler out of the game.
Detwiler gave up four runs, five hits and a walk in 6 2/3 innings.
Randall Delgado lasted only four innings, giving up seven hits and four runs, two earned.
Delgado was hurt by third-inning errors from second baseman Jack Wilson and Simmons, the rookie shortstop, which led to two unearned runs.
Wilson, starting at second base for the first time this season, dropped a grounder by Adam LaRoche for the first error with two outs. Morse singled past Chipper Jones at third. Simmons retrieved the ball in shallow left and threw past Wilson at second base for another error, allowing the runners to advance. Desmond drove in LaRoche and Morse with a single to left.
Detwiler was 0-for-14 this season before his second-inning single drove in Morse, who had singled, for Washington's first run. Flores pushed the lead to 4-0 with his homer off Delgado in the fourth.
The temperature for the first pitch was 101 degrees. ... Braves 2B Dan Uggla, hitting only .156 (12 for 77) in June, received his first day off this season. ... Braves manager Fredi Gonzalez plans to rest Jones on Saturday and C Brian McCann on Sunday. ... Prado did not start. Gonzalez says Prado has been playing with a sore right hamstring. ... Nationals RHP Drew Storen, recovering from a right elbow injury, moved closer to a rehab assignment by throwing to hitters before the regular batting practice. Johnson said Storen could return before the All-Star break. ... Nationals RHP Stephen Strasburg will try for his 10th win when he faces Braves LHP Mike Minor in the second game of the three-game series on Saturday.