Jackman and Shattenkirk scored 1:20 apart early in the second period to put the Blues up 3-1.
Jackman broke a 1-1 tie with a screened one-time shot from the high slot at 1:01 of the middle period with the teams playing 4-on-4. It was Jackman's third goal of the season.
Shattenkirk's goal was on the power play and came on a screened shot from the left point 2:21 into the period. It was Shattenkirk's seventh goal.
Bouwmeester got his fourth goal, 2:14 into the third, when his shot from the left point went in off the Red Wings' Riley Sheahan.
The game was tied at 1 after the first 20 minutes despite St. Louis outshooting Detroit 18-7.
Paarjarvi opened the scoring with 8:47 left in the opening period when he banked one in off Howard's leg on a wraparound from behind the net. It was Paarjarvi's fourth goal.
Nyquist's power-play goal tied the game with 27 seconds remaining in the first. He controlled and put in a loose puck during a goalmouth scramble for Nyquist's sixth goal and his first in nine games.
NOTE: C Darren Helm returned for Detroit after missing 18 of the past 19 games with shoulder and groin injuries. ... St. Louis defenceman Ian Cole is from Ann Arbor, Mich. ... The Red Wings were without C Pavel Datsyuk (lower body), RW Johan Franzen (post-concussion syndrome), RW Daniel Alfredsson (back spasms), D Jonathan Ericsson (ribs), C Joakim Andersson (back), C Cory Emmerton (finger) and G Jonas Gustavsson (groin). ... Blues RW Ryan Reaves celebrated his 27th birthday.