Goals from Steven Davis and Sone Aluko put Rangers two ahead inside 16 minutes on Sunday and Andrew Little justified his selection up front with a composed finish.
Steve Williams headed one back before the break but the champions remained in control and Lee McCulloch netted an opportunistic fourth from his striker's role.
Rangers fans have endured worrying revelations about the club's financial affairs on an almost daily basis since they went into administration on Valentine's Day and the first opportunity for the players to deliver a positive distraction from the crisis ended in a 1-0 defeat by Kilmarnock last Saturday.
The players came into this game knowing there is a real possibility some of them may lose their jobs in the coming week as administrators prepare to review staffing across the club.
But they produced a highly-professional display with a real cutting edge to send the buoyant away fans home happy.
Manager Ally McCoist was forced into a more inexperienced starting line-up after losing Sasa Papac to suspension and Lee Wallace to injury, the left-back joining Steven Whittaker, Kyle Lafferty and Kyle Bartley in the treatment room.
Ross Perry and Salim Kerkar came in for rare starts while Little was preferred to David Healy as he made a first SPL start of the season.
All three acquitted themselves well with Kerkar having a major hand in three of the goals and Perry producing a solid display at right-back.
Inverness welcomed back Gregory Tade from injury with fellow striker Billy McKay also coming in and they made a bright start but Davis scored in the sixth minute with the visitors' first attack.
The Rangers captain began the move before Maurice Edu stretched the home defence with a pass out to Kerkar. The winger played a low ball into the six-yard box and Davis got there first to sidefoot home.
Inverness quickly got in behind the Rangers defence when McKay ran on to Richie Foran's pass. The forward beat Perry inside the box but drove the ball across the face of goal when he had several team-mates awaiting a cutback.
Aluko missed the target with a free header from six yards after Davis had found him at the back post but the winger soon atoned as Rangers went two ahead. The former Aberdeen player fired just inside the post from 18 yards after McCulloch had laid off Little's low cross from the right.
Inverness manager Terry Butcher moved from the stand to the touchline in a bid to sort out his side and Greg Tansey twice threatened from long range, driving just wide before forcing Allan McGregor into a save with a powerful effort the Rangers goalkeeper beat away.
But Edu and Davis were cutting out most of the Inverness attacks before they could reach the penalty box and Rangers moved three ahead with a 36th-minute counter-attack.
Kerkar collected the ball on the left wing and played it through for Little, who got away from the chasing defenders and took his time before finishing from a tight angle with his left foot.
Inverness gave themselves a lifeline four minutes later when Williams rose highest to head home Tansey's inswinging corner from close range. Rangers had disputed the corner award after Tansey's previous effort failed to clear the near post with referee Willie Collum ruling a Rangers player had helped it out.
Tade had a half chance following another Tansey set-piece but he volleyed well over with the last kick of the half.
The striker had a better chance moments after the break after Jonny Hayes got away from Kirk Broadfoot on the right wing and delivered an excellent low cross.
However, Dorin Goian made a crucial intervention as Tade tried to convert from six yards, the Romanian diverting the ball inches wide of McGregor's near post.
Rangers came close to a fourth amid a series of corners, Nick Ross clearing Edu's header off the line before Ryan Esson pushed Davis's follow-up wide.
Esson then saved from Aluko after the winger had held off Graeme Shinnie after running on to Edu's pass.
Caley Thistle moved from a 4-5-1 formation to a 4-4-2 but they were making few inroads as Rangers pressed them high up the park to maintain their territorial advantage.
Kerkar was heavily involved again as Rangers moved further ahead in the 72nd minute. The Algerian worked space to fire an angled drive, which Esson could not hold, and McCulloch ran in to tap home the rebound.
McGregor made a good stop after Tade helped on Hayes' cross but Rangers were otherwise comfortable and McCoist handed game time to Gregg Wylde, Kane Hemmings and Mervan Celik.
McCulloch almost added another when his powerful strike from 15 yards hit the underside of the bar and bounced down off the line following Wylde's corner.