Trailing 1-0 and with a chance to break out with a least a run, Maddon lifted Hendricks for pinch hitter Tommy La Stella in the fifth inning. The move paid off as La Stella drew a walk to load the bases and set up Dexter Fowler's run-scoring sacrifice fly.
"I felt we had to do it right there," said Maddon after the Cubs held on for a 4-3 victory on a frigid night at Wrigley Field. "Tommy was the right guy in that moment. It would have been nice to get more runs -- we had the opportunity -- but getting one was plenty."
Hendricks said he fully understood the move.
"It was a tough day to hit, wind blowing and really cold and how many chances are you going to get?" said Hendricks, who had no decision. "Their guy was throwing really well against us so I completely understand. ... Sometimes situations happen like that."
The Cubs added more in the next inning as Addison Russell's two-run triple gave the Cubs their first lead of the night at 3-1. Russell's triple, his first, drove in Kris Bryant and Ben Zobrist to break a 1-1 tie.
Adam Warren (2-0) worked two relief innings and struck out three to pick up the win for the Cubs (15-5). The Brewers (8-12) dropped their fourth in five games.
Milwaukee starter Jimmy Nelson ultimately took the loss, departing with the score tied at 1-1 with one out in the sixth and runners on first and second.
"The Cubs were pretty patient today," said Nelson, who threw 109 pitches. "They probably only swung at a handful of off speed pitches and they were attacking the fastball and spilling some pretty good pitches. I just walked too many guys and got my pitch count up there."
Brewers reliever Carlos Torres gave up a two-out triple to Russell as the Cubs opened a 3-1 lead.
Nelson (3-2) pitched 5 1/3 innings, allowing three runs (one earned) and two hits. He walked four and struck out six.
Anthony Rizzo made it 4-1 in the seventh with an RBI double to center off Brewers reliever Blaine Boyer.
Brewers pinch-hitter Ryan Braun doubled into the right-field corner off Pedro Strop with one out in the eighth, driving two runs home to cut the deficit to 4-3.
The Cubs had bases loaded with two outs in the bottom of the eighth against Brewers reliever Michael Blazek, who got out of the jam as Jason Heyward grounded to first.
Hector Rondon faced four batters in a scoreless ninth to collect his fourth save.
The game was played in 40 degree weather with 16 mph north winds and a game-time wind chill measuring 34 degrees.
"It's not exactly fun to play in weather conditions like that, but it's just a part of it," said Nelson. "It's just stuff we have to do at the beginning of the season and sometimes at the end of the season. It's not really a crutch."
Nelson didn't allow a hit until Bryant's one-out double down the left-field line in the fourth. He was stranded there as Rizzo struck out swinging and Zobrist popped to left.
The Cubs loaded the bases in the fifth and evened the score on Fowler's one-out sacrifice fly to center that scored Jorge Soler from third.
Hendricks worked five innings, allowing one run and two hits while striking out four and walking one.
"He understood the situation completely and that does not happen every time," Maddon said. "He was pitching great, there was no reason to take him out (but) it's a National League move."
The Cubs have had no rainouts or weather delays this season, but that could change Wednesday night with rain in the forecast. The series concludes with Thursday's scheduled afternoon game.
NOTES: Brewers LF Ryan Braun was out of the starting lineup but pinch hit in the eighth inning. He extended his hitting streak to eight games (14-for-26, .538) after entering the game fourth in the National League with a .364 average. ... Tuesday's game between Chicago and Milwaukee was the first of 19 scheduled games this season. After this week's three-game series, they'll meet again on May 17-19 in Milwaukee. The Cubs were 14-5 against the Brewers last year. ... Chicago C Miguel Montero was a late scratch from the starting lineup, suffering from back stiffness. David Ross worked in his place. ... Cubs RHP Jake Arrieta (4-0, 0.87 ERA) makes his first start since throwing last week's no-hitter in Cincinnati when he faces Brewers RHP Taylor Jungmann (0-3, 8.47 ERA) in Wednesday's middle game. Arrieta was named NL Player of the Week on Monday.