Lyles, who won the 100m in a photo-finish from Jamaican Kishane Thompson in 9.79 seconds, topped his 200m heat in 20.19sec.
The triple world 200m champion had a slow start but as soon as he hit the bend he looked in total control.
The semi-finals are scheduled for 1802 GMT on Wednesday, with the final slated for 1830 on Thursday.
Also going through were fellow 100m finalists Letsile Tebogo of Botswana (20.10sec) and American Kenny Bednarek (19.96) as heat winners.
A third American, Erriyon Knighton, a silver and bronze medallist at the past two world championships, topped another heat in 19.99sec.
And Canada's Andre de Grasse, defending champion and silver medallist at the Rio Games, also qualified, clocking 20.20sec behind Lyles.
South Africa's 400m world record holder and gold medallist in Rio, Wayde van Niekerk, went through after finishing third in his heat, won by Liberia's Joseph Fahnbulleh.
