The Glasgow giant, which lost its place in the top flight in 2012 after a financial meltdown, had won the first leg 2-0 at Ibrox in midweek.
A 1-0 loss on Saturday was enough to ease it through to a final playoff showdown with Motherwell, which finished second from bottom of the Premier League.
Hibs, which was relegated through the playoffs last year, had most of the early pressure with Rangers Cammy Bell by far the busiest of the two goalkeepers
Veteran striker Kenny Miller - who scored one of their goals in the first leg - came closest for the Glasgow side after 25 minutes as the game started to even out, but Hibs should have gone ahead 10 minutes later.
Impressive midfielder Scott Allen burst through the middle and sent Congolese striker Dominique Malonga clear on the left but he could only shoot weakly straight at a relieved Bell.
Malonga went close again as the second-half got underway with a shot that fizzled just inches wide, but Rangers was in general managing to keep the game low-key which was just what it wanted.
Hibs piled forward in search of the goal that would get it back in the contest and it had a succession of desperate appeals for a penalty turned down.
The home side finally broke its goal drought with a superb strike from Jason Cummings deep into injury-time but it came too late in the day as Rangers moved to within two games of playing once again in the Scottish top flight.
If successful it will join Hearts - runaway winner of the Championship which was automatically promoted to replace bottom club St Mirren.
