A first-half Kemar Roofe strike had Gers ahead in the Highlands, before James Tavernier, an own goal and Jermain Defoe added some deserved gloss in the second half.
From the side which twice came from behind to defeat Standard Liege 3-2 on Thursday night to qualify for the Europa League knockout stages, Calvin Bassey and Joe Aribo came in for Borna Barisic and Scott Arfield.
Gers began the match very much on the front foot, moving the ball quickly and with care on what was an excellent surface at the Global Energy Stadium despite some heavy rainfall in the days prior to today’s encounter.
A super free-kick delivery from James Tavernier from deep out on the left ricocheted around the box with Bassey trying to poke it goalwards, but County managed to get bodies in the way to prevent him nabbing goals on successive Sundays.
At the other end, Allan McGregor made a super stop from Harry Paton – the Staggies man cutting in from the right with McGregor brilliantly getting out sharp to narrow the angle and then claw the ball away from Paton’s curling effort.
On 28 minutes, however, Gers hit the front. Steven Davis picked a stunning ball through the home defence wide for the onrushing James Tavernier on the right wing.
He drilled a lovely ball into the six yard box, and sliding in bravely before goalkeeper Ross Laidlaw could claim was Kemar Roofe for his eighth of the season.
It was terrific play from Gers to pick apart what had been, to that point, a very well organised and stuffy Ross County side, with Tavernier and Roofe again showing their quality.
Roofe came close to making it two minutes later – a lovely lay-off from Alfredo Morelos set him up for a vicious strike from 20 yards which only just cleared the bar.
Ryan Kent hit a 25-yard volley wide, while Alex Iacovitti made a fine block to prevent Morelos making it two on the end of a Kent cross just before the interval.
Into the second half, and Tavernier flashed another outstanding ball across the face of goal, while Roofe headed a Kent cross straight at Laidlaw.
A second was coming, and it duly arrived on 56 minutes with that man Tavernier on target incredibly once again for his 16th of the season.
Ryan Kent worked the space well inside the area to cross, and in came Tavernier with all the instincts of a striker to tap home and hand the visitors a deserved cushion.
He then took on a volley which slipped just wide from 25-yards as he looked for number 17, while Connor Randall fired a decent back-post opening over the bar for the Staggies.
Goal number three then arrived on 72 minutes. Connor Goldson played a great ball to the right for Tavernier to run on to – he cut into the area and looked to have set-up Morelos for a tap-in, but before it could reach the Colombian, Callum Morris slid in to put the ball into his own net.
That third goal allowed Gerrard to made four changes – and among them was Jermain Defoe who came on for his 800th career appearance for club and country combined.
Fellow sub Ianis Hagi tested Laidlaw with a decent free-kick effort from out on the right before, fittingly, Defoe got in on the act.
Brilliant work from Cedric Itten on the left took him away from his marker, and he sent a great ball into the feet of Defoe.
He had his back to goal, but as it never seems to do, that didn’t matter a jot as he spun and finished by Laidlaw in the 90th minute.
RANGERS: McGregor, Tavernier, Goldson, Balogun, Bassey, Aribo (Arfield, 66), Davis, Kamara (Zungu, 74), Roofe (Itten, 74), Kent (Hagi, 74), Morelos (Defoe, 74)
SUBS NOT USED: McLaughlin, Barker, Patterson, Barisic.
ROSS COUNTY: Laidlaw, Morris, Gardyne (Hylton, 80), Vigurs, Watson, Iacovitti (Randall, 45), Tillson (Wright, 88), Paton, Donaldson, Stewart, Reid (Charles-Cook, 74)
SUBS NOT USED: Doohan, McKay, Williamson.
REFEREE: John Beaton
Sign Up To RangersTV Today
Rangers TV Monthly - Standard (£6) - Join now to watch exclusive RangersTV content. (Excluding Live Video, Including Live Audio)
Rangers TV Annual - Standard (£60) - Join now to watch exclusive RangersTV content. (Excluding Live Video, Including Live Audio)
CLICK to subscribe to our official YouTube channel and never miss another video: HERE