Jackman, a stay-at-home type who totaled three goals and 12 points in the regular season, joined a rush and scored in transition against Jonathan Quick, last year's playoff MVP. He beat Quick from just inside the blue line for a 2-0 series lead heading to Los Angeles.
The Blues capitalized on a stickhandling goof by Quick to win the opener on Alex Steen's short-handed goal in overtime.
Patrik Berglund's deflection tied it early in the third period for St. Louis, which was swept by the Kings in the second round last season while getting outscored 15-6.
Dustin Brown scored for the Kings, who'll try to rebound in Game 3 Saturday night.
The Kings led 3-0 in every playoff series last year and are down 2-0 in a playoff series for the first time since 2002, when they lost in seven games to Colorado.
The Blues responded after coach Ken Hitchcock called a timeout with just under three minutes remaining. They have won eight in a row at home, allowing one goal in all eight games.
Brown lost his edge on a drive to the net and barreled into Brian Elliott midway in the third period, leaving both players shaken up a bit. Brown recovered quickly enough to stay on for the ensuing faceoff.
Berglund tied it at 3:44 of the third with his fourth career playoff goal, charging the net and having a rebound go off his skate and past Quick. He was skidding to a stop when Quick poke-checked a wrist shot by Alex Pietrangelo and it took less than a minute for the goal to be upheld on video review.
Jaden Schwartz lured Quick out of the net on a break-in a little over a minute later, but didn't get off a shot.
Quick was bent over in pain for several seconds during warm-ups after stopping a shot, then left the ice early. The goalie also spent most of the national anthem bent over as if he were an NFL offensive lineman, but then busily went to work scratching the crease with no evidence he was hurt.
The Kings got off to a much better start in Game 2, carrying the play most of the first period. They needed just 6 seconds to convert on a 5-on-3 advantage for their first lead of the series, with Jackman whistled for interference on the heels of a high-sticking call on Ryan Reaves.
LA's strong play carried over to the second period, with Quick making a nice glove save against Steen on the Blues' lone shot on two power plays; Steen scored the Game 1 winner in overtime.
The Kings threatened on break-ins by Brown and Justin Williams. Brown, among the league leaders with eight power-play goals, then deflected Brad Richards' high wrist shot from the slot and the puck dropped to ice level and slid between Elliott's pads at 9:55. Richards had two goals and three assists during the Kings' three-game sweep of St. Louis in the regular season.
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