In five appearances after joining the club, Broxton was 1-1 with a 9.00 ERA.
Since then, the 28-year-old right-hander has pitched nine straight scoreless outings, dating back to Aug. 21 at Philadelphia.
"Just trying to stay healthy, that was a big thing," Broxton said. "[I've] been able to do that, and then [I'm] just trying to get quick outs -- just trying to cut down my pitch count so my arm doesn't flare up."
Broxton, whose career high of 36 saves came with the Dodgers in 2009, has 108 total saves in eight big league seasons. Before joining the Reds, he had recorded 23 saves in 27 opportunities for the Royals.
With Aroldis Chapman tied for second in the National League with 35 saves, Broxton took on the setup role. Chapman, who is resting a fatigued left shoulder, has been out since Monday. Broxton collected his first save in a Reds uniform on Tuesday.
Cincinnati leads the Majors in bullpen ERA (2.61) and the NL in opponents' batting average (.216).
"He's something special down there," Broxton said of Chapman. "We have a bunch of guys down there that can be closers. But he's our guy, so we're just trying to pick up some innings for him and give him a break."
Broxton picked up his second save for the Reds by closing out the 11th inning of their 5-4 win over the Marlins on Sunday.