Howard saw his first NHL action since injuring a knee Dec. 20 at Tampa Bay.
Tatar scored what proved to be the winner late in the second period and added an insurance goal in the third period to end Detroit's three-game losing streak. He has a team-high 17 goals.
Andreas Athanasiou and Xavier Ouellet also scored for Detroit.
The Blackhawks lost for the second straight night and had their club-record road winning streak end at eight games. Trevor Van Riemsdyk and Artemi Panarin scored for Chicago.
The Blackhawks opened the scoring at 4:23 of the first period on an impressive display of skill by Panarin and Patrick Kane. Just outside the Detroit zone, Panarin slid a backhand pass through defenseman Danny DeKeyser's leg to Kane, who carried the puck into the Detroit end. Kane zipped a quick cross-ice pass to a closing Panarin and he drove a one-timer past Howard.
Detroit tied it with 3:35 left in the period. Using Tatar as a screen, Ouellet drove a rising shot from the point past goalie Corey Crawford for his third goal of the season.
With only eight seconds to play in the second, Detroit regained the lead. Athanasiou accepted a drop pass from Nick Jensen and zipped a low shot by Crawford, who was again screened by Tatar.
The Wings increased their lead to 3-1 15:17 into the second period. Gus Nyquist carried the puck into the Chicago zone and dropped a pass to Henrik Zetterberg. Crawford stopped Zetterberg's shot but Tatar was on the doorstep to smack the rebound home.
A low point shot by Van Riemsdyk beat Howard on the stick side with just 44.3 seconds left in the second period to narrow Detroit's advantage to a goal.
Tatar completed the scoring at 15:31 of the third period. Nyquist forced a turnover along the boards and fed the puck to Zetterberg. He relayed it to Tatar in the high slot and he whipped a shot past Crawford.
NOTES: Including this game, Chicago will close out the regular season with 16 games over a 30-day span. ... Facing his former Detroit teammates for the first time, left-winger Tomas Jurco skated on a line with Marian Hossa and Marcus Kruger. ... Saying he was unhappy with his play in recent games, Detroit coach Jeff Blashill made rookie right winger Anthony Mantha, tied for second on the team with 14 goals, a healthy scratch . . . Defenseman Robbie Russo and forward Mitch Callahan made their Joe Louis Arena debuts as Red Wings . . . The Van Riemsdyk family has scored twice on the Wings this week. Trevor's older brother, James, scored for Toronto in the Maple Leafs' 3-2 win over the Red Wings on Tuesday night.
Blackhawks: Welcome the Minnesota Wild to the United Center on Sunday in a potential showdown for first place in the Central Division.
Red Wings: Host the New York Rangers on Sunday.