Rangers have now lost twice in five days, and have seen their 40-game unbeaten run in the Scottish Premiership ended.
Steven Gerrard's side lost to Malmo in Champions League third qualifying round on Tuesday before falling to a 1-0 defeat to Dundee United at Tannadice in their second Premiership outing of the campaign.
Panic won't set in quite yet for the Ibrox side, who won their first Premiership match 3-0 against Livingston at home. However, it does end a remarkable run which saw them win the Premiership unbeaten last season, ending Celtic's hopes of a historic 10 league titles in a row.
Jamie Robson's 64th minute strike was enough to take all three points against the reigning champions in what was an impressive display from the home side.
Rangers fielded a strong team, with just four changes from the midweek game against Malmo, as Gerrard brought in Mclaughlin, Kamara, Aribo and Morelos for McGregor, Arfield, Wright and Itten.
All eyes now turn to the massively important second leg of their Champions League qualifier at Ibrox this Tuesday as they look to overturn a 2-1 deficit and move one step closer to the group stages.