On p. 150 of The Complete Book of Baseball’s Negro Leagues, John Holway writes:

I haven’t found a 20-strikeout game, but I did find Cyclone Joe Williams striking out 13 New York Giants at Dyckman Oval, New York, on October 9, 1920:

 
(Brooklyn Daily Eagle, October 10, 1920)

This game does not appear in the list of Williams’s starts against major league teams published in Holway’s Blackball Stars (p. 78), so it may be that this game hasn’t been noticed by researchers before (anybody who knows otherwise can say so in the comments.)

Overall, the Giants fielded a major league-quality team, though they were certainly not at full strength. In the lineup were four regulars—Larry Doyle, George Kelly, Earl Smith (who shared catching duties equally with Frank Snyder), and Benny Kauff (by plate appearances the fourth outfielder, but a better hitter than Lee King and at least as good as George Burns).  Not appearing: Burns, Dave Bancroft, Frankie Frisch, and Ross Youngs, whose places were taken by utility men Al Lefevre, Fred Lear, and Miguel Angel (Mike) González, along with pitcher Rosy Ryan in right field.

On the mound was Jesse Barnes, who could be considered the Giants’ ace in 1920 (he led in innings pitched, won 20 games, and had the lowest ERA among the starters); after four innings he was relieved by Pol Perritt, who was only 28 but already winding down his major-league career.

For the Lincolns, “Thomas Jenkins” is of course Clarence “Fat” Jenkins.