The Cubs were leading 2-0 on Tuesday night after four-and-a-half innings -- the minimum for a regulation game.
They were eventually awarded the victory after the field of play was deemed unplayable after a rain delay of four-and-a-half hours.
But after the Giants' successful protest Wednesday, the contest will be completed on Thursday at Wrigley Field in Chicago.
The Giants, who are in the thick of the playoff race, claimed that not enough was done to dry the infield in a timely manner.
"We appreciate Major League Baseball's careful review of our protest that will allow last night's game to be continued tomorrow," Giants president Larry Baer said in a statement.
The protest was apparently upheld under the rule that says games will be suspended and completed at a future date if it is halted by the malfunction of lights or of a mechanical field device under control of the home club.
The contest will pick up in the bottom of the fifth inning with the Cubs batting.
This is the first game protest upheld since the Pirates won a claim that a game in Pittsburgh against St. Louis ended prematurely on June 16, 1986.