Chicago defeated Dallas for the second consecutive time this season, following a 15-game winless streak (13-0-2) against the Stars that dated to March 2002.
The Blackhawks beat Dallas 2-1 on Nov. 29 in Denis Savard's debut as coach. They are now 9-3-3 under Savard, who took over after Trent Yawney was fired on Nov. 27.
The Blackhawks also snapped an 0-for-18 power-play slump that spanned four games. They entered the game with the third-worst power-play conversion rate in the NHL (11.4 per cent).
Stu Barnes scored for the Stars.
Marty Turco made 22 saves in losing for only the second time in his career to Chicago. He is 11-2-1 against the Blackhawks - he lost to them for the first time on Nov. 29.
Arkhipov's five-on-three power-play goal opened the scoring with 1:46 left in the first period. It was the Blackhawks' first power-play goal in four games and 18 chances.
After Turco made a glove save on Adrian Aucoin's shot from the right point, he dropped it. Arkhipov pounced on the loose rebound and scored from the right edge of the crease.
Barnes tied it one-all 2:05 into the second period. He skated out unchecked from the left corner and beat Khabibulin between the pads from the edge of the crease.
Lapointe gave Chicago the lead with 5:15 left in the second. Standing in front of the crease, he managed a mid-air deflection of Arkhipov's shot from the top of the right circle.
Khabibulin made a point-blank save on Niklas Hagman midway through the third and withstood a Dallas flurry around the crease a couple of minutes later. Mike Ribeiro had a close-in chance that slid past Khabibulin but was cleared away by defenceman Brent Seabrook.
Notes: Dallas C Eric Lindros missed the game with an upper body injury sustained in the morning skate. ... C Mike Modano missed his 10th game with a groin/hip injury. ... Chicago C Jeff Hamilton missed his second straight game with the flu. LW Karl Stewart missed his second game with a sprained knee and will be out two to four weeks.