The Hawks won all its games from the Bucks for the first time in 16 years. Atlanta moved past Chicago into the fifth-seeded position in the playoff standings.
Smith and Teague scored 24 points each in bringing Atlanta its second straight win.
Milwaukee owned a 19-point advantage early in the second half and still led by seven going into the fourth period.
Al Horford added 18 points and 17 rebounds for the Hawks, who made it a two-possession game when Horford hit two free throws with 17 seconds remaining.
Monta Ellis had 27 points and a career-best 17 assists for the Bucks. Milwaukee has lost three in a row and 13 of 18.