Goals from Lassana Coulibaly, Ryan Kent, James Tavernier and Glenn Middleton moved the hosts up to fourth as Gerrard quickly eradicated an unwanted record of Rangers' worst league start in 29 years.
Dundee remain rooted to the foot of the table without a single point after five games, and it was an another afternoon for former Rangers striker Kenny Miller to forget.
Miller was dismissed from his role as player-manager at Livingston after just two league games last month and was sent-off in just his second game for Dundee for a late challenge on Borna Barisic 11 minutes from time.
Rangers close to within two points of Celtic, who were held 0-0 at St. Mirren on Friday night.
But it is Hearts who continue to lead the way as Steven Naismith rounded off his fine week with the only goal in a 1-0 win at Motherwell.
Naismith's stunning early season form earned him a Scotland recall and he was on target in the 2-0 Nations League win over Albania on Monday.
At club level, the former Rangers and Everton forward now has eight goals in nine games as Hearts opened up a five-point lead at the top with a fifth straight win.
Livingston's fine form since parting ways with Miller continued as they beat Hamilton 1-0 for a third consecutive win to move alongside Celtic in second.
Hibs edged Kilmarnock 3-2 in a thriller at Easter Road to climb into the top six.
Aberdeen have been Celtic's closest challengers for the past four seasons.
But the Dons languish in eighth with just one league win from their opening five games this season after a 1-1 draw at St. Johnstone.