Goals from Kevin Kyle, Manuel Pascali and Craig Bryson turned the game on its head but the hosts led for just three minutes before Jon Daly completed the scoring midway through the second half.
Calderwood would have been encouraged by the spirit on show as his side fought back from Craig Conway's double, which came after Kilmarnock defender Simon Ford had levelled Prince Buaben's opener.
United finished the stronger team in Peter Houston's first game since his permanent appointment as manager, but they had to settle for their second draw in succession despite scoring seven goals in four days.
The frantic action began from the off and Kilmarnock goalkeeper Cammy Bell made two saves before Kilmarnock threatened in the seventh minute when Mehdi Taouil's powerful strike was pushed away by Dusan Pernis after Kyle had teed up the Moroccan 14 yards out.
Midfielder Liam Kelly, making his first Kilmarnock start, saw his deflected shot fizz just wide but the hosts fell behind in the 16th minute.
Ford failed to clear a throw-in and Buaben slipped past him before slotting a composed finish into the far corner.
The defender atoned four minutes later when he rose well to head home Bryson's corner.
Kelly soon forced Pernis to push over his well-hit strike following a Kyle knockdown and headed over from the resulting corner.
Bell got down well to hold David Goodwillie's drive following a Daly lay-off but he was soon beaten on 27 minutes. Goodwillie's right-wing cross found Conway at the far side of the box and his controlled volley bounced into the corner of the net.
Conway netted his second in the 33rd minute when he dispossessed Gavin Skelton 18 yards out and lifted the ball over Bell.
Skelton paid the price by making way for Conor Sammon and Killie immediately threatened.
Ford's powerful volley smashed into the face of central-defensive partner Manuel Pascali before Danny Invincibile saw the ball cleared from his feet two yards out after Kyle had headed Garry Hay's cross into the danger zone.
But Kyle soon met Hay's 41st-minute corner to head down and into the net with Sammon's swipe in the goalmouth at least putting Pernis off.
Some more poor defending from the hosts allowed Darren Dods an early second-half chance but the defender was off target from close range following Swanson's low cross.
Pascali scooped Kyle's knockdown well over the bar from 10 yards, but the Italian atoned in the 55th minute when he met Bryson's near-post corner and guided an angled header in off the bar.
Invincibile's powerful shot was beaten away by Pernis as Killie continued to press and they went in the 63rd minute thanks to Bryson's stunning strike.
Taouil fed the midfielder after his right-wing corner had been half-cleared and Bryson volleyed the ball over Pernis and into the far top corner.
But Daly soon converted from the penalty spot after Ford had tripped Conway a yard inside the left edge of the box amid little danger.
Conway and Bryson had decent efforts saved at either end before Goodwillie shot inches wide as the Kilmarnock defence backed off.
United looked the stronger team in the latter stages but headers from Dods and substitute Damian Casalinuovo failed to trouble Bell and both sides deserved a point for their effort, if not their defending.