Summer signing Dado Prso secured victory for Rangers after a nervous 90 minutes for under-pressure Ibrox manager Alex McLeish and his side.
Prso headed home from 15 yards after 17 minutes and a Jean-Alain Boumsong header crashed off the crossbar.
But home defender Maurice Ross also struck his own woodwork.
Rangers' Stefan Klos pulled off a couple of superb saves to keep his boss in a job before Caley Thistle's Grant Munro was sent off late on.
Some commentators were tipping McLeish for the sack should they fail to defeat the SPL newcomers from the Highlands.
Paolo Vanoli and Peter Lovenkrands had replaced Gregory Vignal and Shota Arveladze in the home starting line-up after their midweek Uefa Cup disappointment.
Rangers put unchanged Caley Thistle under early pressure, but Barry Wilson threatened a shock with a volley from outside the box just wide of Stefan Klos' left-hand post in the 12th minute.
Former Ibrox youth goalkeeper Mark Brown tipped away a Craig Moore header as Rangers pushed forward again.
From the resulting corner, Moore flicked on to Prso, who made no mistake with his header to give Rangers the lead after 17 minutes.
Ibrox full-back Maurice Ross came close to heading into his own net but was relieved to see the ball bounce back off the underside of the bar after a corner.
Rangers midfielder Dragan Mladenovic had to be stretchered off to be replaced by Stephen Hughes in the 37th minute.
The Inverness crossbar was next to be rattled, by a Jean-Alain Boumsong header.
Nacho Novo headed a good chance wide as Rangers failed to extend their lead before the break.
Prso was on the end of a Ricksen free-kick to the back post, but Brown was able to get behind his on-target header.
There was a let-off for Rangers in the 56th minute when Graham Bayne set up Hart for a great chance, but with only Klos to beat he could only fire across goal and agonisingly wide.
Burke went down in the box at the other end, but referee Calum Murray was not interested in awarding a penalty.
Klos dropped a Juanjo corner, but the ball was scrambled clear.
The goalkeeper then had to divert a back header from Boumsong behind for a corner as Caley Thistle finished the stronger side.
Munro was sent off in stoppage time for a second yellow for fouling Prso on the edge of the box.
Rangers: Klos, Ross (Khizanishvili 45), Moore, Boumsong, Vanoli, Burke, Ricksen, Mladenovic (Hughes 34), Lovenkrands, Novo (Arveladze 61), Prso.
Subs Not Used: Graeme Smith, Vignal, McLean, McCormack.
Goal: Prso 17.
Inverness CT: Brown, Tokely, McCaffrey, Munro, Golabek, Wilson, Keogh, Hart, McBain, Bayne (Hislop 60), Juanjo (Prunty 77).
Subs Not Used: Fraser, Dods, Duncan, Proctor, Black.
Referee: C Murray