Both teams had made mass changes following their Co-operative Insurance Cup exploits for the clash at Tannadice.
Allan McGregor reclaimed the gloves for Rangers, while David Weir, Davis, Kris Boyd, Steven Naismith and Kenny Miller were all drafted back into the side after the midweek win over Dundee.
Youngster Danny Wilson retained his place in the team, with Madjid Bougherra and Lee McCulloch both still out injured.
United also made changes after crashing out of the cup to St Johnstone, with Nicky Weaver, Darren Dods, Craig Conway, Jennison Myrie-Williams, Damian Casalinuovo and Paul Dixon all starting.
On-loan Rangers defender Andy Webster was among those who dropped out of the side as a result of the terms of his loan deal.
Torrential rain proved difficult to cope with from the outset and the floodlights were already on despite the lunchtime kick-off.
Rangers carved out the first real chance when Miller tried to pick out Boyd as he raced into the box but he just failed to connect at the back post.
United were denied the opener when Mihael Kovacevic saw his header crash off the crossbar before the Rangers defence eventually managed to clear the danger.
The Scottish champions then came close themselves when Kyle Lafferty squeezed between two defenders only to stab narrowly wide, before Casalinuovo's header flashed across the face of goal and past the post at the other end.
United should have opened the scoring when Myrie-Williams embarked on a run down the right flank before teeing up the shot for Prince Buaben, but he blasted over from 16 yards.
Instead it was Rangers who surged into the lead with 29 minutes gone. A lovely ball from Sasa Papac was collected by Davis at the back post before he rifled a shot past Weaver in the United goal.
The home side were again denied by the woodwork as they attempted to haul themselves back into the game when Dixon's powerful free-kick from 25 yards smacked off the crossbar.
A Conway corner then sparked a goalmouth scramble but there were no takers to prod over the line as Rangers held onto their slim advantage heading into half-time.
Referee Tumilty and his assistants assessed the state of the pitch at half-time, before Rangers assistant manager Ally McCoist also emerged to check the conditions.
And there was then disappointment for the Rangers fans in particular when the match was duly abandoned.