Hearts were beaten for the first time this season as Craig Sibbald snatched Falkirk a shock 3-2 win at Tynecastle.
Jason Cummings hit his first professional hat-trick in Hibernian's thrilling 3-3 draw with Falkirk at Easter Road.
Falkirk scored a late winner through David McCracken to secure a 1-0 victory over Hibernian.
Scottish Cup holders St Johnstone will face Queen of the South in this season's fifth round, with the Old Firm kept apart.
Hearts extended their lead at the top of the Scottish Championship after claiming a 2-1 victory over Falkirk.
Kenny McDowall praised youngster Lewis Macleod who played a starring role as Rangers hammered Falkirk 4-0 at Ibrox.
Rangers netted three times in 13 minutes as they wrapped up a 4-0 Scottish Championship victory over Falkirk at Ibrox.
Holders St Johnstone have been paired with fellow Premiership side Ross County in the fourth round of the Scottish Cup.
Live only on
More of the games that matter on Sky Sports
Listen to the latest Transfer News
All the gossip from the morning editions
Predict six scores to win the £250,000 jackpot!
Pick your Sky Sports Fantasy Football team