Caretaker boss Peter Houston watched his side dominate the first half at Tannadice on Boxing Day, only for Jon Daly - twice - and David Goodwillie to produce close-range blunders.
Sean Dillon also hit the bar and Damian Casalinuovo also missed a golden opportunity, while Killie twice saw goals chalked off as they gained a valuable point in their battle against the drop.
Houston made just one change from Levein's final team selection as United manager.
The caretaker boss left out Darren Dods for Mihael Kovacevic, who had been dropped from the side that failed to take the field at Hamilton last weekend after the match was called off 15 minutes before kick-off.
Killie made three changes from their damaging home defeat toalkirk, handing Manuel Pascali his first outing for more than a month, as well as recalling Gavin Skelton and Ryan O'Leary.
Houston, Levein's long-time assistant who is set to be invited to join the new Scotland manager's coaching staff on a part-time basis, has been handed the United reins until a permanent replacement for the 45-year-old can be found.
Today was his first chance to show he has what it takes to be that man.
The match kicked-off under light snowfall, nothing compared to the freak storm that led to United's game at New Douglas Park being called off.
Danny Invincibile was close to connecting with a wicked cross from Kilmarnock captain Kevin Kyle inside the opening minute before David Goodwillie somehow failed to convert an even better ball from Craig Conway at the other end.
Conway's corner was then headed over by an under-pressure Garry Kenneth, who also saw another effort from a Paul Dixon free-kick cleared by James Fowler.
Simon Ford and Sean Dillon then suffered a clash of heads in the United box, which resulted in the former writhing around in agony before being carried off on a stretcher and replaced by Jamie Hamill.
United should have scored just after the half-hour mark when Daly's header from Dixon's corner allowed Skelton to clear off the line.
Dillon was then desperately unlucky when his dipping 25-yard drive clattered off the bar before a real howler from Daly saw him fail to stab Jennison Myrie-Williams' first-time lay-off into an empty net.
Invincibile twice almost made the home side pay before the break, failing to control the ball when all alone in the box before seeing a goal chalked off for a foul on Nicky Weaver.
United could easily have found themselves a goal down eight minutes into the second half had Pascali directed a free header on target.
The home side withdrew Goodwillie for Danny Cadamarteri 11 minutes in before the game's first major flashpoint saw Skelton and Kenneth booked for squaring up after the latter went down in the box.
Killie had the ball in the net for a second time in the 67th minute when Kyle nodded home but the offside flag had already been raised.
United, who were in dire need of some inspiration, threw on Danny Swanson for Conway.
The substitute's first contribution was winning a free-kick which saw Invincibile yellow-carded.
The home side made their final change with 16 minutes remaining, bringing on Casalinuovo for Daly.
United finally got a shot on target but Cadamarteri's angled effort was straight at Mark Brown.
At the other end, Kyle sent a shot wide on the turn before Killie brought on David Fernandez for Mark Burchill.
Casalinuovo, who scored twice at Rugby Park last month, wasted a glorious chance seven minutes from time when he shot straight at Brown from 10 yards.
Then, in stoppage time, the Argentinian striker saw an overhead kick turned round the post.