German clubs' poor performance in European competition has raised concerns that the Bundesliga is in decline.
Woakes took three wickets for no runs in nine balls as Pakistan slumped to six for three in pursuit of a target of 352.
The three-time road cycling world champion held off late-charging Travis McCabe of USA Cycling on Sunday to stretch his record for stage wins in America's premier stage race to 17.
Lyles's blistering 9.86sec was the best time this year and a personal best, and lays down a marker ahead of the world championships in the autumn and the Tokyo Olympics next summer.
Ducati duo Danilo Petrucci and Jack Miller will join the Honda rider on the Le Mans front row.
Naomi Osaka's lead in the rankings remains in peril, although reigning French Open champion Simona Halep dropped down to third.