Desmond King returned an interception 90 yards for the punctuating touchdown as the Chargers (5-6) moved within 1½ games of AFC West-leading Kansas City after starting 0-4 while the Chiefs won their first five.
The defending NFC East champion Cowboys (5-6) lost their third straight by at least 20 points, all without star running back Ezekiel Elliott, in a damaging defeat for their fading playoff hopes.
Dallas, playing its 50th Thanksgiving game, finally ended a touchdown drought at a team-record 10 quarters on Rod Smith's 2-yard run early in the fourth quarter.
Keenan Allen had a career-high 172 yards on 11 catches with a touchdown, giving him 23 grabs for 331 yards and three scores in the past two games.
