The right-hander struck out a career-high 13 and walked one in his first major league complete game.
"It was nice to finally shake the catcher's hand at the end of the game," Arrieta said. "That's something I've wanted to do my entire career."
He was five outs from the first no-hitter at Wrigley Field in 42 years when Phillips drove an 0-2 pitch to deep left-center, just beyond the desperate dive of center fielder Matt Szczur on the warning track.
"I was planning on running through the wall if I had to," Szczur said. "I was close."
It was the third time this season Arrieta has flirted with a no-hitter.
He carried a perfect game into the seventh inning against Cincinnati on June 24 before Billy Hamilton singled. In his next outing, Arrieta held Boston hitless until Stephen Drew singled with two outs in the eighth.
When asked whether he believed Arrieta would ever finish the job, Cubs manager Rick Renteria responded with an emphatic "Yes!"
"As a baseball fan, this is one of the things when you come to the ballpark, you might get a chance to see something special," Renteria said. "I thought that outing was pretty special."
Soler has five home runs and 15 RBIs in 14 games this season.
"I was not getting the location the way I want," Cueto said. "That's baseball -- sometimes you have good outings and bad outings, and today was a bad outing."
Cueto yielded six runs and five hits in 5 2/3 innings. He struck out eight.
Milt Pappas threw the last no-hitter at Wrigley Field, an 8-0 victory for the Cubs over San Diego on Sept. 2, 1972.
Arrieta retired 21 of the first 22 batters he faced before allowing Phillips' double. He issued a leadoff walk in the fourth to Hamilton, who was caught stealing on the next pitch.
"He was very good," Reds manager Bryan Price said of Arrieta. "He was very sharp, was able to hit that low zone. There was some real bottom, borderline pitches that he was able to nail with some consistency."
Arrieta has allowed two or fewer runs in 18 of his 24 starts this season. Previously, the longest outing of his career was May 2, 2012, when he pitched eight scoreless innings for Baltimore against the New York Yankees.
Cubs: OF Arismendy Alcantara injured his right hand making a game-saving catch against the outfield wall Monday. Alcantara, who had a wrap on his right hand and wrist, was held out of the starting lineup. "Right now, it's just soreness," Renteria said.
Reds: First baseman Joey Votto took batting practice for the first time in nearly two months as he tries to work his way back from a left quadriceps injury. Votto, who hasn't played since July 5, also took grounders for the second straight day.
ONE RING CIRCUS
The fan who caught Soler's home run ball in the seventh had his celebration cut short when his wedding band flew off his finger and onto the warning track as he was giving high-fives to others in the left-field bleachers. A Cubs security ambassador confirmed that a groundskeeper found and returned the ring shortly afterward.
GETTING HIS HACKS
Touted catching prospect Kyle Schwarber, selected fourth overall by the Cubs in this year's draft, has hit 18 home runs in three minor league stops since June. He took batting practice with the team before Tuesday's game. "On the field, you saw how quickly his bat translated," president of baseball operations Theo Epstein said. "It's a special bat."