Hearts captain Steven Pressley watched from the bench and must have been unimpressed by a lacklustre display from both sides.
Nacho Novo (right) scored the only goal of a poor game
Paul Hartley was handed the armband but could not help the Tynecastle side fashion many chances in a dire first half littered with stray passes.
Rangers spurned a glorious chance after four minutes when Karl Svensson got in the way of Hutton's goal-bound header.
Nacho Novo scored the winner in 78 minutes with a deflected drive.
Pressley was named on the substitutes' bench for the game against Rangers following his controversial omission from the squad against Falkirk.
Hartley replaced Saulius Mikoliunas while Ibrahim Tall took the place of Christos Karipidis.
Rangers made one change to the side that defeated Dunfermline last week, Kris Boyd replacing Lee Martin.
Hearts fans sang Pressley's name as the game kicked off, while the captain watched the action from the bench.
Pressley watched the defeat from the bench
But it was Rangers who made the stronger start when Hutton's header hit team-mate Svensson.
Zaliukas headed away the resultant danger to give the home defence a chance to regroup.
The opening 10 minutes were scrappy as neither side could find a passing rhythm.
Hutton was booked on 16 minutes following a rash challenge on Brellier as Hearts sought to raise the tempo of the game.
Ferguson played a neat one-two before feeding the ball to Novo, whose shot was palmed away by Craig Gordon for a corner.
Gordon had a scare after 25 minutes when Dado Prso beat him to a through ball but could not convert the chance.
Hemdani was the best player on the park in the opening half hour and invariably found a team-mate with a pass while others around him were less composed in possession.
Prso went close with a header on 40 minutes but it sailed just over the crossbar.
Zaliukas was then booked for a late tackle on Ferguson as referee Dougie MacDonald allowed play to continue but Prso could not capitalise.
Clement received a yellow card on the stroke of half-time as the scrappy play continued.
Hearts fans were keen to show solidarity with the club's captain
Velicka almost gave Hearts the lead from the restart, but his shot from just inside the 18-yard box was saved well by McGregor.
Ferguson then forced a great save from Gordon as the Rangers captain tried to impose himself on the game.
Gordon somehow beat out a Boyd effort from six yards with 23 minutes left.
But Novo got an unlikely goal after 78 minutes when his shot deflected off Berra into the net to clinch victory for the Ibrox side.
Hearts: Gordon, Barasa, Berra, Tall, Zaliukas, Aguiar, Brellier, Wallace (Goncalves 48), Hartley, Velicka, Mole (Mikoliunas 60). Subs Not Used: MacDonald, Pressley, Neilson, Jankauskas, Karipidis.
Booked: Zaliukas, Hartley.
Rangers: McGregor, Hutton, Svensson, Hemdani, Smith, Novo, Ferguson, Adam, Clement, Kris Boyd, Prso. Subs Not Used: Klos, Buffel, Papac, Rae, Sionko, Sebo, Martin.
Booked: Hutton, Clement, Novo, Smith, Kris Boyd.
Goals: Novo 78.
Ref: D McDonald.