Arrieta gave up three runs and four hits in 7 2-3 innings. He struck out six and walked three.
The right-hander is 4-0 with a 1.30 ERA in his last seven starts.
Arrieta said he has taken more of a leadership position after Samardzija and Hammel were traded to Oakland last week.
''I am pretty comfortable with the responsibilities that come along with a role like that. It's something I embrace and look forward to continue to be in this role, to help guys establish themselves and combat the struggles that take place at this level,'' he said.
''Hopefully, help guys start to take off and produce at a high level for us,'' he said.
''The future is bright. That is very apparent. Guys like Alcantara and we have guys in the pipeline that can definitely help us in the future,'' Arrieta said.
The Braves, who scored the tying run in the top of the ninth on Christian Bethancourt's two-out single, have lost five of six following a nine-game winning streak.
Jordan Schafer stole three bases for Atlanta and was caught stealing once.
''Schafer had a great day. He stole three bags, he got on base, played nice defense. And BJ (Upton) been doing nice in the leadoff spot. I'm happy with those guys at the top of the order. Now we need to keep the line moving, and we will,'' Braves manager Fredi Gonzalez said.
Arrieta left with a 4-3 lead but wound up with a no-decision when Cubs closer Hector Rondon (2-3) couldn't hold the lead in the ninth.
Rondon allowed a leadoff double to Jason Heyward in the ninth. After retiring the next two batters, Rondon gave up Bethancourt's single. It was Rondon's third blown save of the season.
The Cubs have won two straight after losing six in a row.
''We were probably a little down a little bit after losing those two guys. They were two big guys in the clubhouse. But we have a tight group and we all pull for each other. We will be all right,'' Ruggiano said.
Freddie Freeman drove in two runs for Atlanta.
Braves starter Alex Wood pitched 5 1/3 innings and allowed four runs on five hits and three walks. The 23-year-old left-hander struck out six.
''I battled through some stuff. I thought we battled hard and scraped for some runs. I thought we played pretty well,'' Wood said.
After retiring the first six batters, Wood gave up a leadoff double to Chris Coghlan in the third inning. Coghlan stole third and scored on Arrieta's perfectly executed squeeze. With two outs, Ruggiano's single drove in Mike Olt to make it 2-0.
Arrieta was unable to hold the lead. He walked Schafer in the fourth and gave up his first hit of the game, a double to Simmons. Freeman and Justin Upton had RBI grounders.
In the sixth, Wood reached on an infield single, his first hit in the majors, and moved up on Schafer's sacrifice bunt. With two outs, Freeman doubled off the ivy in center field for a 3-2 lead.
The Cubs loaded the bases with no outs in the sixth. Junior Lake struck out and broke the bat over his knee. Coghlan hit a tying single and Braves reliever Shae Simmons walked Luis Valbuena on four straight pitches to give the Cubs a 4-3 lead.
NOTES: Cubs INF Emilio Bonifacio started his rehab assignment in Arizona. He's been on the DL with an oblique strain since June 13. ... Rizzo appreciated all the support he got in the push by the team that made him the final NL All-Star voted in by the fans. ''Walked over to the offices, thanked all the front office and the people working behind the scenes to pump it up, to promote it. Very, very appreciative. My family's ecstatic. Come along way, altogether - me, myself, everyone else around me that's coached me, that's helped me out through good times and bad times. It's an accomplishment I'll cherish forever,'' the first baseman said. ... Cubs 2B Darwin Barney was activated from the paternity list. The Cubs recalled Zac Rosscup from Triple-A Iowa and relievers Kyle Hendricks and Blake Parker were optioned to Iowa. ... Braves starter LHP Mike Minor is scheduled to make his second career start against the Cubs on Saturday. In his previous start, he gave up one run in 7 1/3 innings.