The Indians claimed a 2-1 lead in the Series, which resumes Saturday with a second straight game at Wrigley Field.
Crisp lined a one-out single to right field off Cubs reliever Mike Montgomery to drive in pinch-runner Michael Martinez.
Indians reliever Andrew Miller (1-0) collected the win after striking out three and allowing no base runners in 1 1/3 innings of relief.
Edwards Jr. (0-1) took the loss, giving up two hits and the lone run in 1 2/3 innings.
Chicago was shut out for the fourth time in the postseason, tying a record set by the 1905 Philadelphia Athletics. The Cubs managed just five hits against four Indians pitchers.
The Indians had base runners but no results in each of the first two innings.
Hendricks' pickoff of Francisco Lindor and a strikeout of Mike Napoli helped Chicago get out of the first. After Ramirez reached on a second-inning infield single, Perez grounded into an inning-ending double play.
The Indians made a more serious bid in the fourth as Lindor led off with a single to right and was eventually perched at third with two outs following a Ramirez single and Lonnie Chisenhall's fielder's-choice grounder to first.
But Hendricks quelled the threat with a called third strike on Perez on a 3-2 count after Perez had fouled off two previous pitches.
Hendricks got into a more serious jam in the fifth as Tyler Naquin led off with a single to left -- the third inning the Indians put a leadoff runner on. Carlos Santana reached on a one-out walk as Hendricks neared 80 pitches.
Reliever Justin Grimm entered and quickly saw an 0-2 count on Lindor go to 3-2 before he got the Indians shortstop on an inning-ending double play.
Hendricks gave up six hits, walked two and struck out six in 4 1/3 innings.
Indians starter Josh Tomlin held the Cubs to one base hit through the first five innings and allowed just three balls out of the infield.
He gave up a leadoff single to Jorge Soler in the fifth, got the next two batters on grounders -- including a Baez sacrifice -- and departed in favor of Miller.
Miller extended his run of scoreless innings to 14 as pinch-hitter Miguel Montero flied to right to end the inning.
Tomlin allowed just two hits, struck out one and walked one in his 4 2/3 innings.
NOTES: The Game 3 winner has gone on the win the World Series 37 times (64.9 percent), including in four of the last six Fall Classics. ... Indians manager Terry Francona's 9-0 record in World Series games was tarnished by Wednesday's 5-1 loss to the Cubs. ... The Cubs lost their most recent World Series game at Wrigley Field before Friday on Oct. 10, 1945, a 9-3 decision in Game 7 against the Detroit Tigers. Their most recent World Series win at Wrigley came on Oct. 8, 1945, an 8-7, 12-inning win over Detroit. Since 1945, 45 other big league parks have hosted World Series games. ... After going 3-for-7 (.429) with a double, two walks and two RBIs as the DH in two World Series games, OF Kyle Schwarber is limited to pinch-hitting duties in Chicago. While medically cleared to bat and run the bases, doctors would not clear Schwarber to play the field. He had knee surgeries after an outfield collision in early April and was idle until this week. ... Cleveland sends RHP Corey Kluber (3-1, 0.74 ERA) against Chicago RHP John Lackey (0-0, 5.63 postseason) in Saturday's Game 5. Kluber was the Game 1 winner as the Indians blanked the Cubs 6-0 last Tuesday at Progressive Field. Probable starters for Sunday's Game 5 are Cubs LHP Jon Lester (2-1, 1.69) opposite Indians RHP Trevor Bauer (0-1, 5.00).