The captain and his Kings specialize in agitating and outworking the opposition -- and even after they blew a three-goal lead, they drew one more penalty to set up the winner.
Brown scored twice during the Kings' three-goal first period, and Carter had three points in Los Angeles' sixth straight home victory over Ottawa in the past decade. After scoring just six goals in their first three games of the season, the Kings were on their game again.
"We just wanted to establish that mentality we had last year," Brown said of last season's Western Conference finalists. "Obviously, it wasn't as clean as we wanted it, but we got the job done. That's what we need from our power play, to step up at big times. The important thing is to continue to build on that."
Milan Michalek scored the tying goal for the Senators with 4:27 left in regulation. Jean-Gabriel Pageau netted his third career goal in the second period, and Bobby Ryan scored his first goal with Ottawa early in the third.
Carter scored the winner during 4-on-3 play in the final second of Clarke MacArthur's hooking penalty from late in regulation. Richards teed up a shot that might have banked off an Ottawa stick before it was redirected by Carter in front.
"He made a great play," Carter said of his longtime teammate and roommate. "All I did was go to the net and stand there. You go to the net, put your stick on the ice and guys in this league are going to find it. It's pretty simple. I don't do anything pretty out there."
Craig Anderson stopped 28 shots as the Senators opened a four-game Western road swing that is part of their season-opening six-game trip.
Ryan, the longtime Anaheim Ducks forward, scored during a power play early in the third period of his first game back in Southern California since he was traded north. Kings fans booed him loudly out of habit.
"I'm pretty proud of the way the guys reacted to come back and get a point on the road," Ryan said. "This is a tough building. ... My first two games, I felt like there were opportunities where I didn't capitalize. I'm glad it's over with, and now hopefully I can go get a bunch more."
Ottawa captain Jason Spezza sat out to rest a persistent groin injury, leaving his team without its top-line center. He should return for back-to-back games in San Jose and Anaheim this weekend.
Stephane Da Costa replaced Spezza on the Sens' first line between Michalek and Ryan.
Brown got the Kings' first goal moments after he stepped out of the box from serving a penalty for interfering with Anderson, his fellow U.S. Olympic team hopeful and former teammate with the OHL's Guelph Storm.
The Senators then committed a string of penalties, and Carter scored his third goal of the season off a scramble at the moment Los Angeles' first 5-on-3 advantage ended.
Los Angeles went up 3-0 on another goal by Brown, who deflected a pass from Carter in Anderson's crease right after another two-man advantage ended.
"We can't just sit there and say, 'The officials don't like us,' or whatever," Ottawa coach Paul MacLean said. "We've got to quit taking penalties and putting our team in a bad spot out there."
Ottawa answered early in the second period when Erik Condra controlled a loose puck and fed the 20-year-old Pageau for a one-timer that trickled past Quick. Pageau, who had a memorable postseason hat trick against Montreal in May, was playing in just his 12th regular-season game.
Ryan trimmed the Kings' lead to one goal with a power-play score. Moments after Quick made a phenomenal blocker stop on a point-blank chance from Da Costa, Michalek found a loose puck amid a tangle of legs in the high slot and fired it past Quick for his first goal of the season.
Ottawa RW Chris Neil went to the dressing room in the second period after Kings defenseman Alec Martinez accidentally chipped the puck into his face. Neil returned later in the period. ... The Kings scratched D Jake Muzzin after a poor game against the Rangers on Monday night, activating Martinez for the first time this season. LW Daniel Carcillo made his Kings debut on a line with Carter and Richards. Colin Fraser was scratched. ... Los Angeles will begin a four-game road trip at Carolina on Friday night. Ottawa doesn't have its home opener until Oct. 17.