Their second successive win gave them a three-games-to-two lead in the best-of-seven National League Championship Series.
Their second successive win, on a balmy night at Dodger Stadium, gave the Cubs a three-games-to-two lead in the best-of-seven National League Championship Series.
They will try to punch their ticket to Major League Baseball's championship showcase -- and give themselves a chance to end the longest title drought in North American sports -- when they host game six on Saturday.
Game seven, if needed, would be in Chicago on Sunday.
The Cubs have not won the World Series since 1908, setting a futility standard unmatched by any team in any major sport, with some among their long-suffering fans certain the team has been cursed.
Since falling into a 2-1 series hole against the Dodgers, the Cubs have bounced back with a vengeance, displaying the form that saw them win a major league-leading 103 regular-season games.
Russell, who broke out of a 1-for-25 slump at the plate with a home run in Chicago's 10-2 triumph on Wednesday, connected for another two-run blast in the sixth inning on Thursday.
Javier Baez was on second with one out when Russell connected on a high slider from Dodgers reliever Joe Blanton, belting it into the seats in left-centerfield.
Anthony Rizzo, whose three hits Wednesday included a homer, put the Cubs on the board with a run-scoring double in the first inning.
The Dodgers pulled even in the fifth inning when Howie Kendrick doubled with one out and then stole third on Cubs starter Jon Lester's 1-0 pitch to Adrian Gonzalez.
Kendrick was called out, but upon review the call was overturned and he scored when Gonzalez grounded out to first base.
After Russell's blast put Chicago back on top, the Cubs exploded for five runs in the top of the eighth when Dexter Fowler and Kris Bryant singled in runs and Javier Baez's bases-loaded double off reliever Ross Stripling drove in three runs.
The Dodgers chipped away with one run in the bottom of the eighth and two more in the ninth before their rally bid fell short.
Although they'll now have two chances to clinch the series at home, the Cubs will face a tough task on Saturday, when the Dodgers give the ball to left-handed pitching ace Clayton Kershaw.
Kershaw baffled the Cubs in a 1-0 shutout in game two at Wrigley Field, giving up just two hits and striking out six over seven innings.