Miller was brought down by goalkeeper Daniel Bachmann in the 95th-minute but the Austrian dived to his left to save.

Andrew Nelson twice put the hosts in front, either side of Kilmarnock debutant Conor McAleny's strike.

Chris Burke's fine free-kick drew the fourth-place visitors level.

Steve Clarke's side had looked more likely to find a winner, with Greg Taylor and Gary Dicker coming close before the late drama.

But Kilmarnock lost ground on the league's top two - with Celtic and Rangers both winning on Wednesday - although they go level on points with third-place Aberdeen.

A night for the new & the old

This match screamed January window signings. The powerful and bustling Nelson was a constant thorn in the side of Kilmarnock, whose own new man making a debut - McAleny - played a key part as well.

Over and above the goalscorers, though, Jim McIntyre's new additions have turned them into a side that do not look like they should be languishing near the bottom of the Premiership.

Scott Wright was a menace down the left, as was Andy Dales down the right, while Ryan McGowan and Andreas Hadenius have added much to the spine of the Dark Blues.

Nelson brings so much to the Dundee team. Apart from driving the ball low into the far corner for his first, and toe-poking it home from distance for his second, the 21-year-old closed people down and made important flick-ons. He would have had a first-half hat-trick had it not been for a fantastic Bachmann save.

But as well as the new in this match, there was plenty room for the old.

Burke has been there and done that over a varied career, and his free-kick from 25 yards oozed class. The 35-year-old's fitness levels are exceptional and he will enjoy watching his fourth goal of the season.

The crucial kick near the end of the match came the way of another well-travelled attacker in Miller, the player so many managers would want in such a pressure situation, yet he was unable to deliver.

'Dundee have enough to avoid bottom spot' - analysis

Dundee will hope are not left to rue that penalty miss come the end of the season. With Hamilton winning, a Dark Blues victory would have created a five-point gap between them and bottom club St Mirren.

That said, the Dens Park side were impressive for large parts of this match and, with all their new signings, look like they have enough to avoid at least automatic relegation.

Kilmarnock are now three games without a win but did well to come back from behind twice, and up until the penalty, looked the likelier side to grab three points.

'We could have been behind' - reaction

Dundee manager Jim McIntyre: "It's disappointing, obviously. when you've got a penalty to win it in the last minute, but Kenny's scored a lot of important goals for us and we all miss penalties.

"If truth be told, we could've been behind before that last 30 seconds."

Kilmarnock manager Steve Clarke: "We were the team pushing to win it at the end and then we almost shot ourselves in the foot.

"It's difficult to knock the players when they're chasing the points but sometimes you need to be a little bit more professional and realise a point is a good result."