After losing the opening two games of the Western Conference quarterfinal series, the Kings won four in a row -- all by one goal. Los Angeles will face either Anaheim or San Jose in the conference semifinals.
Jonathan Quick made 21 saves to get the victory and has been in goal while the Kings have won each of their last five playoff series. Quick was the winning goaltender 16 times last year as Los Angeles marched to the Stanley Cup championship.
With time running out in the second period, Penner fired a slap shot that eluded Brian Elliott. The goal came an instant before the horn sounded to end the period.
Elliott faced only 16 shots in the Blues' final game of the season.
Los Angeles joins Chicago and San Jose in the second round of the Western Conference playoffs. Anaheim and Detroit will determine the other team to advance from the West when they meet in a Game 7 on Sunday.