The Jambos looked to be on their way to success at The Almondvale Stadium, after former Middlesbrough star Phil Stamp (pictured) put them ahead after just eight minutes.
However, Livi pulled level with less than ten minutes remaining when Spanish defender Rubio headed home.
Dundee let a two-goal lead slip at Dens Park as Kilmarnock kept their hopes of a European place alive.
Defender Lee Wilkie (39) and Steven Milne (41) scored two in two minutes just before half time to give The Dark Blues a comfortable lead at the interval.
Scottish 'B' international Peter Canero brought his side back into the game with a goal just five minutes into the second period and the comeback was completed when veteran Gary McSwegan struck with five minutes remaining.
Aberdeen eased their relegation fears as they won the preverbial 'six pointer' at Motherwell 1-0.
The only goal of the game came from the penalty spot after seven minutes when midfielder Paul Sheerin blasted home.
Well pushed hard for a reply, but all they had to show for their efforts was a red card for Stephen Pearson late into the second period.
Click below for match summaries::
Dundee 2-2 Kilmarnock
Livingston 1-1 Hearts
Motherwell 0-1 Aberdeen
Click here for SPL table
