Rangers plunged deeper into crisis after crashing out of the Scottish Cup as goals from Gavin Gunning and Johnny Russell secured a 2-0 win for Dundee United at Ibrox.
A lack of resources up front following the deadline day departure of Nikica Jelavic was painfully evident as the Gers ended this tie with a front pairing of Salim Kerkar and Andrew Little - one player who has never started a game for the club and another who has been injured for the best part of the last 18 months.
Russell had the ball in the net for United after a couple of minutes but the effort was disallowed when referee Willie Collum ruled goalkeeper Allan McGregor was fouled by Jon Daly in the build-up. However, United were celebrating with 15 minutes gone when Gunning met a Gary Mackay-Steven cross and sent a firm header past McGregor from eight yards.
The visitors scored again after 35 minutes when Dixon slipped the ball into the path of the unmarked Russell and he took advantage of the space to rifle high past the grasp of McGregor.
Rangers had already exited the Champions League, the Europa League and the Scottish Communities League Cup, meaning the league title is now their only hope of silverware this season.
Hearts and St Johnstone will meet again in a fifth-round replay after drawing 1-1 at Tynecastle.
Hearts struggled to build on the advantage created by winger David Templeton's tenth-minute goal and, after Francisco Sandaza headed against the bar and Dave MacKay was sent off for two bookable offences, Cillian Sheridan equalised after 77 minutes.
The teams will now meet in a replay at McDiarmid Park on February 14.