Redick, acquired by the Milwaukee Bucks at last month's trade deadline, scored his new team's first eight points in the extra period. He finished with 17 as the Bucks beat the Utah Jazz 109-108.
''I was just taking what was there. I didn't feel like I was struggling at all (in regulation),'' Redick said. ''I got good looks and the ball was in and out a lot of times. I never feel like I'm struggling. I always feel like the next shot is going in.''
Milwaukee coach Jim Boylan said he has extreme confidence in Redick's ability to make shots.
''The guy is a great shooter. I know he missed a couple but the thing with J.J., when he shoots the ball, you expect it to go in,'' Boylan said. ''Whenever I see him raising up for a shot, I feel pretty good.''
Monta Ellis scored 34 points to lead Milwaukee, which won its fourth consecutive game after dropping three in a row following the All-Star break.
''(Monta) has been great,'' Redick said. ''He was sensational again tonight. He shot the ball really well from all over the floor. He's a great player when he's in attack mode like he's been in the last few games.''
Ellis, last week's Eastern Conference player of the week, finished 15 of 21 from the field.
''He's a big shot maker. He likes big moments and he made a couple great plays for them in big moments of the game,'' Utah coach Tyrone Corbin said. ''In the overtime, we had opportunities and made a couple rotation mistakes there and Redick got open and hit two threes.''
Brandon Jennings had 20 points and 17 assists for Milwaukee, while Larry Sanders chipped in with eight points, 16 rebounds and six blocked shots.
Jennings has 36 assists in the team's last two games.
''The easiest thing in the NBA is scoring. Trying to assist and count on guys to get buckets for you is the hardest part,'' he said. ''Everybody didn't think I could pass like this. I've always been a pass-first point guard since high school, so now we have a little more help with J.J. so I can show what I can do.''
Derrick Favors tied a career high with 23 points and added 15 rebounds for Utah, which lost for the fourth time in five games. Paul Millsap had 22 points and 14 rebounds, Alec Burks added 19 points and Enes Kanter had 18 points.
''We had some lapses on defense and they got some open 3s and on the road, that's tough,'' Millsap said.
Millsap made a layup to start the overtime period but Redick hit a 3-pointer to give the Bucks the lead. He drained another 3-pointer with 47 seconds remaining to give the Bucks a 107-105 advantage.
DeMarre Carroll hit one of two free throws to cut the lead to 107-106 before Ellis nailed a jumper over Carroll from around the top of the key to give the Bucks a 109-106 lead with 14.7 remaining. Kanter's putback of Millsap's missed 3-point shot cut the lead to 109-108 with 1.6 remaining. Following a timeout, the Bucks were able to run out the clock.
The game marked the first time that the Bucks have played consecutive overtime games since December 2009. It was the first time Milwaukee had played in and won back-to-back overtime games since February 1991.
The Bucks moved within one game of the Boston Celtics for the seventh seed in the East playoff race.
''I think when you play in these close games and you win, it can't help but boost your confidence,'' Boylan said. ''We're getting more comfortable with each other out there.''
The Jazz held a 99-96 lead late in regulation before Jennings drained a 3-pointer from the wing with 8.4 seconds remaining to tie the score. Gordon Hayward's shot in the lane was altered by Sanders and Kanter missed a put back, forcing overtime.
''(Hayward) had a straight line drive to the basket,'' Sanders said. ''I saw him and I tried not to swipe down, not to foul and keep my hands high.''
Milwaukee, which trailed by three points at halftime, appeared to gain control of the game with a 21-6 run over the first 8 minutes of the third quarter to take a 66-54 lead. The Bucks held their biggest lead of the quarter at 73-60 and maintained at 75-65 margin at the end of the period. Ellis had 11 third-quarter points for Milwaukee.
''It's kind of one of our re-occurring themes that we've got to break, bad habits coming out of halftime not ready to play,'' Millsap said.
The Jazz held a 24-20 lead after the first quarter, paced by Favors' 15 points and nine rebounds. In the quarter, Utah outrebounded Milwaukee 18-9 and held an 11-0 advantage on second-chance points.
Utah built an eight-point late in the second quarter but a 3-pointer by Ersan Ilyasova cut the lead to 48-45 at the half.
Favors had 17 points and 14 rebounds in the first half to lead Utah. Jennings had 10 first-half assists.
The Jazz continue their road trip Wednesday night at Cleveland.