Poor marking allowed Ryan Kent and Filip Helander to head the home side into a healthy lead before Joe Aribo’s fine finish before half-time.
Ryan Jack scored his return from injury before Connor Goldson’s headed finish.
They could even afford a missed penalty from James Tavernier as they remain unbeaten in the league this season.
County struck woodwork twice after the break, but by then Rangers were well on their way to their ninth win in a row over the side who remain third bottom of the table.
John Hughes’ side had arrived buoyed by last week’s 4-1 thumping of Aberdeen, but they never looked in danger of spoiling the occasion for Gerrard as he became the fastest-ever Rangers manager to reach his 150th game in charge – his 926 days beating Dick Advocaat by 24 hours.
By bravely handing 17-year-old Leo Hjelde – signed on loan from Celtic 24 hours earlier – his debut and dropping winger Regan Charles-Cooke and forward Jermaine Hylton, Hughes had signalled his intent to keep it tight.
County’s high press did manage to trouble Rangers – but only for the six minutes it took for the hosts to score with their first foray into the Highlanders’ box.
Hjelde was too late on the scene as Kent looped in a finish after being found unmarked by Alfredo Morelos’ header across the face of goal.
Top scorer Tavernier blotted his copybook by having a weak spot kick saved by Ross Laidlaw, although justice was probably done as Morelos looked to be fouled outside the area.
Rangers remained relentless and Kent fired a low effort against a post before Helander shrugged off his marker to rise in space and head home a Borna Barisic corner.
The defending was similarly poor as Aribo sidestepped Charlie Lakin and Iain Vigurs before a sublime curling finish.
County started the second half with plenty of purpose and midfielder Harry Paton sent a low drive off the inside of a post and centre-half Alex Iacovitti should have done better than loop a header off the bar when found unmarked at a free-kick.
Gerrard responded with a clutch of substitutions and one of the replacements, Jack, fired low past Laidlaw before Goldson rounded off the scoring with a stooping header from a corner.
It was perhaps a fitting flourish considering the centre-half has featured in 142 of Gerrard’s games in charge.
