Hearts manager Craig Levein watched his side from the stands at Fir Park after recovering from a recent health scare and saw striker Steven Naismith grab the only goal of the game midway through the first half.
"I thought our base strength was our defending, and our two young centre-halves were nothing short of amazing," Levein told the club's website.
Hearts will fancy their chances of making it six wins from six next week when they host Livingston, who sit level with Celtic on 10 points after a 1-0 home win over Hamilton.
Rangers, still smarting from defeat to 'Old Firm' rivals Celtic in their last match, were 3-0 up at half-time against bottom side Dundee thanks to goals from Lassana Coulibaly, Ryan Kent and a James Tavernier penalty.
They made it 4-0 through substitute Glenn Middleton with seven minutes left and while the result pleased manager Steven Gerrard the former Liverpool great said there was plenty of room for improvement.
"We got our joy with early goals but at that time that is when I'm looking for players in my team to be a bit more relentless and ruthless and really go for teams and split the game in two," he told the club's website.
"When you are 2-0 up so early, go and get three and four before half-time. I just thought the game died at certain times, the tempo and the intensity dropped too much for my liking."
(Writing by Peter Rutherford in Seoul; Editing by Greg Stutchbury)
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