Rangers gave departing manager Alex McLeish a winning send-off against a second-string Hearts side.
Hearts' fringe players made a real game of it but Kris Boyd ensured he would finish as Rangers', and Kilmarnock's, top scorer with a goal in either half.
His first was a back-post header from Peter Lovenkrands' corner.
Ronald Waterreus made a series of good saves before Boyd stroked the ball into the net following good work Gavin Rae, to give McLeish a fitting farewell.
The early stages suggested the match would be an open affair, with both sides creating good opportunities.
Rudi Skacel flashed a shot across the face of goal in the first minute and Marvin Andrews' volley from 12 yards was blocked by Martin Petras.
Dado Prso then sidefooted wide of goal when he should have hit the target and Skacel warmed Waterreus' gloves with a stinging drive.
Michal Pospisal must have thought he had scored after 21 minutes when he got his head to Mirsad Beslija's cross, but Waterreus did superbly to get down at his right post to palm the ball away.
Referee Iain Brines infuriated the home support by awarding Prso a free kick for a foul by Petras when the Croatian striker had retained possession and was clean through on goal. The resultant set piece came to nothing.
Kyrgiakos congratulates Boyd on his opening goal
Steve Banks did well to turn the ball round the post from Boyd's close-range shot after 35 minutes following a good run by Chris Burke. But the keeper was at fault as Peter Lovenkrands corner evaded him and Boyd made no mistake as he headed in at the back post.
Waterreus had to be alert again six minutes after the break to beat away Beslija's near-post shot after the winger had made good progress down the right.
The Dutch keeper made another excellent stop on the hour, denying Skacel with his legs as the Czech shot on the turn at close range.
Lovenkrands blasted wide at the near post when he should have gone across goal, and he was nearly punished as Bruno Aguiar drilled in a fierce effort from 25 yards, only for Waterreus to push it away and Pospisal to slide the rebound wide.
Boyd doubled his tally for the afternoon, after a fine run and slide-rule pass by Gavin Rae, as he side-footed the ball past Banks.
Soto Kyrgiakos somehow headed over from Burke's cross before Waterreus, who had earlier hurt a hamstring, was replaced by debutant Lee Robinson, who showed safe hands in the closing minutes to keep the clean sheet.
Rangers: Waterreus (Robinson 78), Murray, Andrews, Kyrgiakos, Smith (Alex Rae 49), Burke, Hemdani, Gavin Rae, Lovenkrands (Buffel 68), Kris Boyd, Prso.
Subs Not Used: Malcolm, Novo, Lennon, Ashikodi.
Booked: Kris Boyd.
Goals: Kris Boyd 36, 74.
Hearts: Banks, Barasa, Petras, Berra, Wallace, Brellier (Johnson 62), Beslija (Mikoliunas 81), Aguiar, Skacel, Elliot, Pospisil (Makela 75).
Subs Not Used: Gordon, Neilson, Camazzola, Cesnauskis.
Booked: Petras, Barasa, Skacel, Pospisil, Makela.
Ref: I Brines