Luckily for Hudson, the hard-throwing Samardzija began having control problems, and the Atlanta Braves took advantage of the situation.
"You know you're not going to get much against a pitcher like Samardzija," Hudson said. "He was throwing some cheese in there."
Chicago ended a six-game road trip with four losses as it heads to Wrigley Field for the home opener against Milwaukee on Monday.
Hudson (1-0) allowed three hits, one run and two walks in 6 2/3 innings. He struck out seven while improving to 3-1 in seven career starts against the Cubs with a 3.12 ERA.
"That's Hudson," Chicago manager Dale Sveum said. "He changes speeds. He's got a slider, cutter, curveball, split. His fastball is really deceiving sneaky and obviously he can get groundballs. That's Hudson."
Samardzija (1-1) set a career high with 13 strikeouts, but gave up four hits, four runs and four walks in 5 2/3 innings.
"He's got good stuff and he's a great athlete and one heck of a competitor," Uggla said after going 0 for 3 against Samardzija with two strikeouts.
"Everybody knows that. He kept us off balance. You've got to respect his 97 (mph fastball). We were able to scratch a couple (of runs) across, and Huddy was able to hold them right there."
The Braves, without injured starters Freddie Freeman and Andrelton Simmons, had struck out 10 times by the end of the fourth, but they got an offensive lift for the second straight game from Ramiro Pena, a reserve shortstop batting in the No. 8 spot.
In the fifth, Samardzija retired the first two batters before Pena doubled and Hudson walked. With B.J. Upton batting, a wild pitch advanced both runners. Samardzija then walked Upton on a wild pitch that scored Pena and made it 1-1.
In the sixth, Justin Upton whiffed for the 13th strikeout, but Samardzija loaded the bases with two outs on Uggla's fielder's choice and Juan Francisco's single before he hit Chris Johnson with a pitch.
Samardzija was unhappy with home plate umpire Alfonso Marquez, running toward the plate to argue that the ball had missed Johnson.
"I don't know," Samardzija said. "I'll have to go back and check the replay. We were just trying to go up and in, and I guess it grazed him."
Pena, the next batter, singled into right field to drive in two runs to make it 3-1 and chase Samardzija. Hudson followed with an RBI single off reliever Michael Bowden to give the Braves a 4-1 lead.
"Our bench is so deep that you can run Pena in there and not lose a beat," Braves manager Fredi Gonzalez said. "And put Chris Johnson at first base and still put a pretty good team on the field. That's a sign of a good baseball team. Well-rounded."
Avilan stranded two runners in the eighth when Nate Schierholtz grounded out.
Uggla's homer, his second, made it 5-1. Braves reliever Jordan Walden struck out the side in the ninth.
Sveum said before the game that RHP Carlos Marmol has been removed as closer in favor of RHP Kyuji Fujikawa. Neither pitched Sunday. ... Braves 1B Freeman was upset with the team's decision to place him on the DL with a strained right oblique. He will stay in Atlanta for treatment and will not accompany the Braves on their six-game road trip that begins Monday at Miami and continues Friday at Washington. ... One night after hitting his fifth homer in five games, Justin Upton struck out four times. ... Samardzija's previous strikeout high was 11, a mark he first set last July 2 at Atlanta and matched last Aug. 13 against Houston. ... Samardzija is 2-1 with a 2.75 ERA in three career starts against the Braves. ... Atlanta's Simmons, who's missed two games with a sprained right thumb, hopes to return to the lineup early in the week. ... Cubs RHP Matt Garza, on the disabled list with a left side strain, threw a bullpen session, but is still a few days away before he begins a rehab assignment. ... Sveum said 2B Darwin Barney is a couple of days away from a rehab assignment and could return April 15 against Texas.