And after an indifferent first-half display at Caledonian Stadium, they did just that with three good goals after the break to see off their Highland opponents.
Mendes set the ball rolling with a brilliant finish just 24 seconds into the second period before Kris Boyd sealed a good victory with a late brace.
It was crucial to come home triumphant and having done that, Gers have shown there’s a long way to go in the championship race.
Walter Smith’s men began well and Nacho Novo was proving to be a dangerous option on the left wing.
Indeed, it was good work from the Spaniard which presented the Light Blues with their first chance after he won a corner off David Proctor.
When Steven Davis’ initial inswinger was returned to him, the former Fulham midfielder set up Madjid Bougherra and he steered just past the post.
It didn’t take the visitors long to put the ball in the net but despite appearing to break the offside trap when Davis released him, Kenny Miller’s effort was disallowed.
Back came Caley Thistle, who might have had chances through Andrew Barrowman and Iain Vigurs had it not been for good tackles by David Weir and Kirk Broadfoot.
The Highlanders tried to make a game of it and were able to, though that was due to Gers taking longer to find their rhythm than they’d have liked.
With that said, Smith’s side almost went ahead in spectacular fashion after 12 minutes thanks to Novo’s wonderful vision.
He spotted home keeper Ryan Esson off his line and shot from the halfway line, beating the ex-Aberdeen man but also just clearing the crossbar.
Inverness had the best opportunity in the early stages to go in front when Vigurs met Roy McBain’s cross and headed towards goal.
But Allan McGregor was equal to the task and made a magnificent save to deny the home midfielder from point-blank range.
The keeper was called into action again when Barrowman caught sight of goal and once more Rangers were thankful to their man between the posts for keeping the score level.
As a fuse blew and the floodlights went out, it seemed the away side were still searching for a spark too as play raged on regardless.
Novo tried to give them it as he charged down a clearance then gave Davis the ball but when he got it back, the striker’s lob went straight to Esson.
Gers started to look a bit more threatening again and Davis found the target but also had Esson in his way when Miller’s perseverance gave him his chance.
With that missed effort, the balance of play swung back to the home team and they finished the half strongest.
Ian Black and Vigurs both came close with long-range attempts while Don Cowie shot over from a tight angle seconds before the interval whistle blew.
Rangers needed more creativity after the break but Smith stuck with the same team that had begun the game initially.
That decision paid off as within 24 seconds of play getting underway again, they went in front with a great goal from Mendes.
While captain Barry Ferguson lay on the ground nursing an apparent head knock, Novo carried on down the left flank and skipped away from two men.
He then played inside with the outside of his right foot and after a neat lay off, Mendes curled past Esson from 25 yards to break the deadlock.
It was a great strike and another to remember after standout counters earlier in the season against Celtic and Partick Thistle.
Inverness tried to level through Barrowman but his flicked header was well over the upright with McGregor looking on intently.
At last, Rangers were starting to look comfortable and going behind so early in the second half appeared to take a lot out of Craig Brewster’s team.
The lively Novo cut in and drilled with his right foot but Esson saved at his near post then hit the target again but was flagged offside.
Gers made their first change as Smith threw on Chris Burke for Miller with just under half an hour remaining.
One of the winger’s first contributions was to set up the previously quiet Boyd, who held off Proctor’s challenge and almost beat Esson but saw his shot stopped on the line.
Rangers were looking more likely to score again, with Caley Jags even lending a hand as Ross Tokely almost put the ball into his own net after Mendes and Novo broke away.
Davis was next to try and he nipped in to clip inches over when Inverness couldn’t clear their lines properly.
Time was getting away from the hosts and that suited the Ibrox outfit as they sought a much-needed victory.
Burke nearly added a bit of gloss as he burst clear of his man and rifled a foot past from 20 yards.
At the other end, the Light Blues were given a reminder they still had work to do as Barrowman’s rocket tested McGregor.
Rangers’ response to that was emphatic as seconds later, with 10 minutes left, Boyd made sure of the three points as he slotted Davis’ pass under Esson with a composed finish.
Not content with that, he then headed in at the back post four minutes from time to bring his total for the campaign to 20 goals.
The three-goal cushion maybe flattered Gers but that won’t worry then and now they’ll look to make up more ground against Falkirk when the SPL resumes on January 17.