Dougie Samuel's men were beaten by two second-half goals in the scorching sunshine.
Samuel included marquee signing Blair Henderson in the starting line-up, the striker having joined from city rivals and SPFL League Two outfit Edinburgh City.
There were also places in the starting XI for returning duo Jamie Dishington and Michael Herd.
The Glasgow side enjoyed the lion's share of possession in the opening stages without really putting pressure on goalkeeper Blair Carswell, although the Spartans No.1 did well to stop an Arron Lyall effort.
Dishington saw a header drop wide of the far post ten minutes before the break, but the visitors got their noses in front within two minutes of the restart, Cole McKinnon's well-placed effort beating Carswell.
Rangers continued to pose a threat and they doubled their advantage midway through the second half when Robbie Ure showed great composure to round Carswell and slot home despite the protests of offside from the Spartans players.
Elsewhere, Civil Service Strollers edged a five-goal thriller at Christie Gilles Park to see off a well-drilled Edinburgh University outfit.
The hosts took the lead through Alieau Faye's 25th-minute penalty but the students were level nine minutes later when Ross Maguire finished off Max Condie's cutback.
The uni then turned the game on its head five minutes later through Innes Lawson's cheeky chip to lead at the half-time interval.
Lewis Duffy headed Gary Jardine's men back into the game within 60 seconds of the restart and the same player pounced again to head home the winner with little more than 15 minutes left to play.
Strollers move up to eighth in the standings while the students are tenth. Spartans, who have played a game fewer, are 15th.
Meanwhile, Bonnyrigg Rose will be looking to build on their weekend win over Celtic B when they travel to Broadwood tonight to play hosts Cumbernauld Colts.