The 23-year-old showed no ill-effect from running the 100m final on Monday night, leading her race on the bend and then easing away from fellow competitors on the straight.
With 100m champion Shelly-Ann Fraser-Pryce and reigning two-time 200m world champion Dafne Schippers pulling out of the event, Asher-Smith is now a heavy favourite for gold.
American Brittany Brown suggested she, and not double Olympic champion Elaine Thompson, will be the main rival for the top position on the podium, winning Heat 3 in a personal-best time of 22.33, 0.28 seconds ahead of the Jamaican.
Briton Jodie Williams qualified from Heat 2, despite losing on a dip to Ivet Lalova-Collio, finishing one-hundredth of a second behind the Bulgarian's 22.79.
Anthonique Strachan won Heat 1 in 22.87, Niger Aminatou Seyni finished fast to set a national record in Heat 5 with 22.58 and Anglerne Annelus dominated the final heat winning in 22.56, where Britain's Beth Dobbin also qualified in third place.