The striker took his Irish international goalscoring record to 25 to put his side 2-0 up after only 11 minutes of the Group Four clash at Lansdowne Road.
His goal exuded quality as Spurs team-mate Andy Reid - who played 64 minutes - fashioned a ball in behind the Israeli defence onto the right foot of Robbie who cushioned a volley beyond the stranded keeper.
But it went downhill from there for both Robbie and the Republic.
Injured after being brought down the box after only three minutes - no penalty was awarded - Robbie had a goal disallowed after 25 minutes before departing the action two minutes later, still struggling with that early knock.
Israel pulled a goal back after 39 minutes before levelling from the spot on the stroke of half-time. Ireland streamed forward in the second half without reward and Andy O'Brien was controversially sent off late on as it stayed 2-2.
Robbie has to be a doubt now for Ireland's trip to the Faroe Islands in World Cup qualifying on Wednesday.
Boss Brian Kerr said: "Robbie hit his shoulder on the ground in a challenge from which I thought we should have had a penalty.
"His shoulder is sore and he could not play on. His movement was badly inhibited. We will now have to wait and see how he is going to be."
Ireland are now fourth in Group Four but only two points separates four teams with Switzerland top on 12, Israel on 11 and France and Ireland on 10. Israel have played seven games, the rest six.
Robbie Keane scored but was injured as the Republic of Ireland suffered a setback in World Cup qualifying with a draw against Israel on Saturday.