To compound the disappointment for Robbie Neilson’s side, winger Josh Ginnelly was ordered off in the closing stages of the match for a second caution and will now serve a suspension.
Both teams created opportunities during what was a very open 90 minutes between first and third in the table. However, first-half strikes by Alfredo Morelos and Joe Aribo were the decisive moments which earned the visitors three points.
Hearts competed well and carved out a number of opportunities during the course of the game. Not converting them transpired to be costly, particularly during a second half in which they saw the Rangers crossbar struck twice.
The home side enjoyed 53 per cent possession and had 16 goal attempts to the Glasgow team’s 11. Eight of those 16 were on target but, nonetheless, overhauling the visitors’ 2-0 interval advantage proved too difficult.
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That was even more evident once they were reduced to ten men late in the match. Rangers could also have scored more than twice had Craig Gordon not been on form once again. They left the Capital city celebrating the finishing which set them apart.
Rangers hadn’t won any of their last three visits to Tynecastle and arrived on the back of a demanding Europa League trip to Lyon. After a 1-1 draw there, new manager Giovanni van Bronckhorst had a five-match unbeaten run to protect in Edinburgh.
Just over 1,000 travelling fans took up position in the Roseburn Stand to back his team. Hearts reduced Rangers’ previous ticket allocation of 3,400 in order to accommodate more of their own supporters in a move which went down well with the Gorgie locals. They had bought up every seat available to them by kick-off.
The teams warmed up in MND Scotland t-shirts to publicise the charity after the disease claimed the lives of former Hearts captain Marius Zaliukas and ex-Rangers skipper Fernando Ricksen.
As is always the case when either of the Glasgow two are in town, an intense atmosphere enveloped Tynecastle. Hearts needed the points to close a nine-point gap between them and the league leaders, who were seeking to increase a four-point advantage over second-placed Celtic.
The afternoon’s first scoring chance fell to Liam Boyce, who collected John Souttar’s long forward delivery in behind the visiting defence. He tried to loft the bouncing ball over Allan McGregor but the Rangers goalkeeper pushed it over his crossbar.
It was a decent chance which Hearts were made to regret when the opposition converted from their first attack on nine minutes. Ryan Kent evaded Taylor Moore on the left flank before a deep cross which Fashion Sakala collected. He skipped past Cammy Devlin and cut the ball back for Morelos to dispatch it into the net.
Sakala should have added his own name to the scoresheet seconds later at the back post. However, Rangers waited only moments to strike again. Connor Goldson’s long ball out of defence was perfectly controlled on the run by Aribo, who ruthlessly fired it beyond Gordon as Souttar chased.
With only 13 minutes played, Hearts were 2-0 down and facing a considerable task to get back into this match. Rangers’ exercised a strong grip on their two-goal advantage and looked more than capable of scoring again with the speed of Kent and Sakala out wide.
Boyce and Ginnelly both tried attempts at McGregor’s goal which landed wide of either post after the half-hour. Then, from Devlin’s slid pass, Boyce was presented with another opportunity in the inside-right channel. This time he forced McGregor into a strong save low to his left.
At half-time it was obvious Hearts needed to score the next goal in order to have any chance of salvaging something from this game. A well-drilled corner routine ended with Gary Mackay-Steven shooting from a tight angle, however McGregor’s fingertips were equal to the task.
The veteran keeper was beaten on 52 minutes when Calvin Bassey stretched out a leg attempting to clear Ginnelly's driven cross. He succeeded in deflecting the ball onto his own crossbar and, as it bounced down before being cleared, one sensed nothing was going Hearts’ way.
Gordon prevented a third on 59 minutes by blocking Scott Arfield’s shot after the midfielder sprinted through on to Morelos’ pass. Scotland’s No.1 was down again to stop Sakala’s strike following a blistering turn of pace by the Zambian to carry the ball away from Hearts defender Stephen Kingsley. Then Gordon stopped another attempt from Morelos.
Rangers had increased the tempo in search of a third goal. The hosts responded and carved out another chance when Mackay-Steven cut the ball back for Boyce, whose first-time shot on the turn landed in the Gorgie Road end.
Again the crossbar reverberated on 72 minutes when Kingsley’s angled free-kick rebounded off it. Frustration boiled over for Hearts ten minutes from the end when Ginnelly received a red card.
Devlin’s challenge on Borna Barisic prompted an angry reaction and Ginnelly got involved in a face-to-face confrontation. Both he and the Croatian were booked by referee Nick Walsh and, having been issued a yellow card in the first half for dissent, Ginnelly headed for the tunnel.
An impressive late double save by McGregor thwarted the Hearts substitute Ben Woodburn and his team-mate Boyce. For all their efforts, there was no breaching the Ibrox club’s rearguard.
Hearts (4-2-3-1): Gordon; Moore, Souttar, Halkett, Kingsley; Devlin (Gnanduillet 86), Haring; Ginnelly, McKay, Mackay-Steven (Woodburn 74); Boyce.
Rangers (4-3-3): McGregor; Tavernier, Goldson, Bassey, Barisic; Arfield, Kamara, Aribo; Sakala (Lundstram 82), Morelos (Wright 72), Kent.
Referee: Nick Walsh.