The Frenchman hit home in the 71st minute to give Newcastle victory at the eighth time of asking and cap an unconventional day at St James' Park.
Kick-off on Tyneside was delayed by an hour due to issues with the newly installed big screen at St James' Park, with engineers scaling the stadium walls to fix the issue and ensure the game went ahead.
Once the game did get under way Newcastle enjoyed the better of the proceedings, though a lack of composure in front of goal looked likely to cost them - typified by Papiss Cisse missing an open goal.
But Obertan ensured Cisse's profligacy was not punished by netting his first goal since October 2012 to ease some of the pressure on under-fire manager Alan Pardew.
A first maximum haul of 2014-15 moves Newcastle within a point of the teams immediately above the drop zone - including neighbours Sunderland after their 8-0 mauling at Southampton earlier in the day.
The pre-match drama continued as Cheick Tiote was injured in the warm-up and replaced by Vurnon Anita, supplementing Pardew's only other change which saw Steven Taylor replace Mike Williamson in defence.
Newcastle settled better after the bizarre events leading up to kick-off and Fabricio Coloccini curled a seventh-minute effort narrowly wide.
Matty James returned to the midfield along with Esteban Cambiasso in two of Leicester's three changes and the 23-year-old wasted an opportunity to punish some slack Newcastle defending as he shot straight at Tim Krul.
For all Newcastle's dominant possession, they were perhaps fortunate not to concede a penalty in the 28th minute when Daryl Janmaat appeared to illegally impede Leonardo Ulloa as the Argentine forward sought to get on the end of a dangerous cross in the area.
Leicester began to get a foothold in the game in the latter stages of the first half, with only the woodwork denying them the opener in the 38th minute when Marc Albrighton's cross-cum-shot struck Krul's left-hand post.
Pardew's side emerged with renewed confidence after the half-time interval, Moussa Sissoko seeing an effort deflected wide before Cisse could only find the side-netting from a tight angle after rounding Kasper Schmeichel.
Jack Colback saw a fierce free-kick turned over the bar by Schmeichel but Obertan's moment of magic finally put the hosts into a deserved lead.
The former Manchester United man cut in from the left and avoided three Leicester challenges before unleashing a superb low shot out of Schmeichel's reach to his right.
An end-to-end finish saw each side come close but Newcastle ultimately hung on and the habitual ill-feeling at the final whistle of their games was finally lifted as Pardew celebrated a long-awaited success.
