After a scoreless first period, Lehtinen gave the Stars the lead 2:25 into the second. Dallas nearly scored again, but Stars forward Jason Arnott knocked the net off and wiped out Pierre Turgeon's goal.
Carolina answered with five seconds left in the second period when Jeff O'Neill tied it. O'Neill, set up by Sean Hill and Ron Francis, earned his 400th NHL point in Saturday's win at Boston.
Lehtinen put the Stars back on top 2-1 by scoring a short-handed goal at 9:32 of the third period.
The Hurricanes, who had a two-game winning streak snapped, tried for the tying goal but couldn't beat Marty Turco.
But with 3:08 remaining, Brenden Morrow sealed the victory for Dallas with his seventh goal of the season. Lehtinen earned the only assist.
Dallas hadn't won at Carolina since the teams first met on Jan. 3, 1998.
Turco made 16 saves to even his record at 14-14-4. Kevin Weekes stopped 24 Stars but fell to 10-11-6.
|Jere Lehtinen (3) Tip-in - ASST: Brenden Morrow (14), Teppo Numminen (7)|
1 - 0 DAL
|Jeff O'Neill (4) Wrist shot - ASST: Ron Francis (6), Sean Hill (7)|
1 - 1 Tie
|SHG - Jere Lehtinen (4) Tip-in - ASST: Mike Modano (13), Don Sweeney (3)|
2 - 1 DAL
|Brenden Morrow (7) Backhand shot - ASST: Jere Lehtinen (3)|
3 - 1 DAL
|Pierre Turgeon Holding against Eric Staal|
|Erik Cole Tripping against Brenden Morrow|
|Josef Vasicek Hi-sticking against Scott Young|
|Erik Cole Holding the stick against Brenden Morrow|
|Brenden Morrow Hooking against Bret Hedican|