Hamza Igamane and Danilo were on target in the first-half in Dingwall, before captain James Tavernier sealed the points late in the game.
From Wednesday evening’s convincing 6-0 victory over Kilmarnock there was one change as Connor Barron came into midfield in place of Mohamed Diomande.
That meant Rangers lined-up with Jack Butland in goal behind a back four of James Tavernier, John Souttar, Leon Balogun and Jefte.
Barron joined Nico Raskin and Ianis Hagi in midfield, while Vaclav Cerny, Hamza Igamane and Danilo provided the attack.
Rangers threatened early in Dingwall, with Jefte driving down the left before delivering a ball into Cerny inside the box.The winger controlled it before getting a strike away at goal but it was just high of the target.
With six minutes played, Rangers had the lead in a fantastic start for Clement’s men. Jefte and Igamane combined on the left, with the Moroccan striker releasing a superb shot from the edge of the box and looping it over the goalkeeper and into the top corner for his fourth goal in four games.
The home side looked to continue to make it difficult for the visitors, but Rangers were still carving out some good opportunities as they looked for a second goal. Danilo sent a ball across the pitch in search of Vaclav Cerny, with the winger taking a good touch before looking to get into the box to get a shot away but the Ross County goalkeeper Jack Hamilton was out to smother the ball, before Danilo was just over the target with an effort in the area.
It wasn’t all one-way traffic though, and at the other end, Ross County showed their threat as they came close to an equaliser. Noah Chilvers found himself in space on the edge of the box and forced a good save from Jack Butland as he tipped wide the strike.
Vaclav Cerny was again stopped by Jack Hanilton as the goalkeeper came out to deny the winger a shot after he latched on the end of a pass from Danilo.
The pressure did pay off for Rangers and it was 2-0 with 37 minutes played as Danilo was alert to pounce on an opportunity. Josh Nisbet played a routine ball back to the goalkeeper but Hamilton took a heavy touch and the Brazilian was there to nick the ball and get a toe to touch it over the line.
Into the second-half, Ross County had an opportunity from a corner as Akil Wright headed just wide from the deflected set piece to send it out for another corner.
From the next corner, County again threatened and it was Wright again who got the first connection on the ball as he sent a header towards goal but Jack Butland did well to block.
Cerny forced a save from Hamilton shortly after as the goalkeeper got low to push away the strike from the winger.
With 20 minutes remaining, Clement turned to his bench for the first time of the afternoon as he introduced Nedim Bajrami and Dujon Sterling in place of Danilo and Vaclav Cerny, with Mohamed Diomande and Cyriel Dessers on for Connor Barron and Hamza Igamane.
Bajrami forced a good save from Hamilton as the match headed into the final few minutes.
Rangers did have a third, and it was captain James Tavernier who found the back of the net with a fantastic finish. Another shot from Bajrami was blocked by a Ross County defender before Tavernier followed up with an unstoppable hit to make the final period more comfortable in Dingwall.
It was another good victory for Rangers on the road, as attention now turns to the visit of Tottenham Hotspur in the UEFA Europa League on Thursday evening.
RANGERS: Butland, Tavernier, Souttar, Balogun, Jefte, Raskin, Barron (Diomande, 79), Hagi (Dowell, 86), Cerny (Sterling, 70), Igamane (Dessers, 79), Danilo (Bajrami, 70)
Subs: Kelly, Ridvan, Propper, McCausland.
Ross County: Hamilton, Wright, Allardice (Grieves, 82), Randall, Hale (Brophy, 65), Chilvers (White, 46), Harmon (Reid, 78), Campbell, Nisbet, Efete (Brown, 46), Samuel.
Subs: Amissah, Leak, Loturi, Telfer.