Hernanes and Rodrigo Palacio put a sub-standard Inter two goals up before half-time, but the Amaranto responded well with Paulinho and Innocent Emeghara earning them a deserved point which took them to within a point of safety.
Inter coach Walter Mazzarri will have to provide club president Erick Thohir with more reasons for a third game in a row without a win which takes them just two points clear of Parma, who have a game in hand against Roma on Wednesday.
It was far from vintage football from Inter, although they still created the better chances in the first half with Hernanes' left-foot shot on the turn only just passing wide of the far post from outside the area.
Three minutes later, Livorno's on-loan forward from Inter, Ishak Belfodil, beat Juan Jesus in the air, but failed to get enough power on his header to beat Samir Handanovic.
Hernanes netted his first goal for Inter in the 37th minute after Mauro Icardi missed his attempted volley from Palacio's header, leaving the ball unwittingly for Hernanes, who was followjng in to lift his shot into the roof of the net.
On the stroke of half-time, Palacio doubled Inter's lead with a fine volley past Bardi, his shot skidding off the ground and past Bardi into the far corner.
Without shining, Inter took what seemed to be a comfortable two-goal lead into the break, although it did not prove to be enough to win the game.
Leandro Greco's corner was turned into the top left-hand corner by Paulinho early in the second half as the Serie A strugglers mounted a recovery.
Inter continued to go through the motions, wasting a chance to restore their two-goal lead when Icardi's shot was saved and the ball fell out kindly to Fredy Guarin.
The Colombian rounded Bardi once, but his shot was blocked, the ball returning for him to dribble past Bardi once again before he shot into the side netting from a tight angle.
With players up in support, it was a chance which Inter should probably have done more with, and Guarin once again showed a lack of vision when he set up Livorno for their equaliser.
The Inter midfielder, who recently extended his contract with the Nerazzurri, gave away possession with a needless pass back towards his own goalkeeper which turned into a perfect assist for Emeghara, who kept his cool to slide the ball past Handanovic, levelling with five minutes to go.
Inter mounted a late charge as Mazzarri held his head in his hands at another chance wasted to cement a place in Europe next season.