Rangers "set a good standard" in shattering Hearts' 10-game unbeaten streak but must be more ruthless, said manager Michael Bale.
The visitors had three goals ruled offside yet still won with plenty to spare as Robbie Neilson's bold attacking gameplan backfired.
Alfredo Morelos netted either side of Malik Tillman's strike to keep Rangers within nine points of Scottish Premiership leaders Celtic.
"I still want more," said Beale.
"We could have scored more. [Hearts goalkeeper] Zander Clark had a good game but we were wasteful at times. We did good things well and we should demand more from each other."
Hearts' chastening defeat trims their advantage in third, with St Mirren now six points back with a game in hand.
The Tynecastle men have now lost seven consecutive meetings with Rangers, who stretch their undefeated start under Beale to 11 games, including 10 wins.
Neilson's front-loaded line-up - including a flimsy midfield three of Robert Snodgrass, Garang Kuol and Barrie McKay - raised eyebrows before kick-off and soon prompted sighs of anguish from the home support as Rangers seized upon the hosts' vulnerabilities.
It was 2-0 going on five or six by the break. Beale's men took fewer than 10 minutes to surge ahead as Ryan Kent burned past Kuol inside the box and stood up a cross for Morelos to head past Zander Clark.
The visitors had efforts from Morelos and Fashion Sakala ruled out for offside either side of the opener, but deservedly doubled their advantage when a short corner was played back to Borna Borisic. The Croat's cross was kept alive by Connor Goldson at the back post and Tillman supplied an adept hooked finish.
Hearts were twice saved by the woodwork - first from Kent, then from a miscued Snodgrass header - before Rangers' hat-trick of disallowed strikes was completed after the break with Sakala again foiled by the flag.
Having tweaked his line-up midway through the first half, Neilson substituted the ineffective Kuol and Hill at the break but there was to be no turning the tide of Rangers' dominance.
Kent won a penalty, then was booked for diving under Alex Cochrane's challenge when the decision was overturned, and only some fine goalkeeping from Clark prevented Hearts succumbing to a hammering amid a glut of Rangers chances.
The scoreline took on a truer reflection when Morelos tucked in Sakala's low delivery and VAR overruled the offside call.
Lawrence Shankland might have claimed a late consolation, clipping a shot inches over, and Hearts knew it wasn't their night when Goldson avoided conceding a penalty when the ball hit his hand in the box.
The Zambia striker did everything but score. Two goals disallowed, an assist, and a performance full of menace. Hearts will be glad to see the back of him
Old Firm derby apart, this looked the toughest assignment of Beale's early tenure, but Rangers negotiated it with aplomb.
They have scarcely delivered a more complete performance under the Englishman. They harried Hearts from the off, never giving them a moment to settle, and kept up the relentless tempo.
Another double continues Morelos' renaissance and in midfield Glen Kamara and John Lundstram provided the steel to allow Rangers' attacking players to flourish.
Hearts' attacking ambitions were quickly nullified and makeshift wing-back Hill endured a particularly torrid time against Sakala. Likewise Kuol floundered in an unfamiliar position.
They left themselves wide open and their poor start left a mountain to climb. They were plagued by mistakes too, with the usually-reliable Stephen Kingsley guilty of gifting possession. He was far from the only culprit in maroon.
Hearts manager Robbie Neilson: "Rangers played well, but we were poor. Rangers pressed us very well, but we still had opportunities to pass and were just 15-20% off it.
"Our decision-making at times was a bit negative. Zander Clark was outstanding and I've got to thank him for keeping the score down."
Rangers manager Michael Beale: "It was a really, really strong performance, first half in particular.
"Overall I'm delighted. We can't drop from that standard now. We should have scored more and have started to keep clean sheets regularly, which is the sign of a good team."
It's another Premiership home outing for Hearts on Saturday, with Dundee United the visitors to Tynecastle (15:00 GMT), while Rangers host Ross County at the same time.