The Lily kicked off on a very heavy pitch and took the lead in the eighth minute with Steven Ferguson firing in a shot from 18 yards out.
Edinburgh United equalised in the 23rd minute from a dubious offside position, Gabrielle Auriemma poking the ball past Lily keeper Steven Hay.
Lily fought back and went ahead in the 40th minute through Gary Fisher.
But in added on time in the first half and with the last kick of the ball, United’s Taylor Hendry looped the ball over Hay’s head from 20 yards to make it 2-2.
The second half was much the same as the first with both teams trying to gain the lead and it was the Lily for the third time in the match who went ahead in the 75th minute after good link up play from Kenny McMillan who found Steve Barrie whose cutback gave Ferguson his second goal with an easy tap in.
United again equalised in the 82nd minute from another poor refereeing decision which awarded them a free kick 20 yards out.
Christopher Hendrie fired his effort into the top corner to give both teams a share of the points.
Next for Easthouses this coming Saturday is a visit down the coast to Dunbar United.
Easthouses: Hay, Moffat, McManus, Hall, Young, Russell, Barrie, Watson, Shearer, McDermott, Ferguson. Sub: McMillan, Tainsh, Taylor. Arthur.