Curtis Joseph made 19 saves for his first victory since March 22 and the Coyotes snapped a five-game losing streak. Joseph's 445th career win moved him within two victories of Terry Sawchuk, who is fourth on the career list.
Bill Thomas and Shane Doan also scored for Phoenix.
Tom Kostopoulos and Michael Cammalleri scored for the Kings, who have dropped six straight.
Roenick gave Phoenix a 1-0 lead at 9:17 of the first when he redirected Derek Morris' blast from the top of the left faceoff circle past Sean Burke for a power-play goal.
Thomas made it 2-0 at 17:48 when he pounced on a loose puck above the right faceoff circle and one-timed a shot over Burke's glove.
The Coyotes finished the first period with a season-high 20 shots on goal.
Kostopoulos cut the lead to 2-1 at 17:23 of the second period, scoring from the right side of the crease after the puck took a long bounce off the end boards. But Doan extended the lead to 3-1 just 75 seconds later when he took a pass from Roenick in stride between the circles and beat Burke with a wrist shot.
The Kings pulled to 3-2 with 11:22 to go when Anze Kopitar's shot bounced off Joseph's right skate on the far left edge of the crease and Cammalleri scored into the vacated net.
Notes: Kostopoulos' goal was his first since Jan. 16, a span of 32 games. ... Coyotes LW Jeff Taffe, who missed the last two games with a sore left foot, played one shift before leaving for the night because of the soreness. ... Kings C Derek Armstrong injured his knee late in the second period and did not return. ... Hall of Famer Dale Hawerchuk was inducted into the Coyotes' ring of honour before the game. Hawerchuk scored 379 goals in nine seasons for the Winnipeg Jets from 1981-90. ... None of the three inductees to the Coyotes' ring of honour the last two seasons ever played an NHL game in Phoenix. ... Coyotes general manager Mike Barnett was booed when he was introduced during the ceremony.