Ireland looked to be heading for defeat with 10 minutes left in Belgrade on Monday, but second-half substitute Murphy headed home Robbie Brady's corner to restore parity for Martin O'Neill's men.
The visitors were ahead for almost an hour following Jeff Hendrick's opener, which found the net via a deflection off Branislav Ivanovic after two minutes.
But on a pitch soaked through by a day of torrential rain, Southampton midfielder Dusan Tadic wreaked havoc in Ireland's penalty area and he provided the assist for Filip Kostic to equalise for Slavoljub Muslin's side.
Tadic then scored from the penalty spot to deservedly make it 2-1 to Serbia, but Ireland rallied late on and Murphy delivered a final twist in a dramatic opening Group D encounter.
Ireland made a great start when Robbie Brady's second-minute free-kick was parried by Predrag Rajkovic and John O'Shea's cross bounced to Hendrick, whose shot found its way past the goalkeeper via the leg of Ivanovic.
Serbia attempted to muster a quick comeback and Filip Kostic drew a smart save from Darren Randolph following a mazy run.
Ireland struggled to provide for lone striker Shane Long, but - while dominating possession - the closest Serbia came to finding the net was from a Matija Nastasic shot that trickled wide after a goalmouth scramble.
Despite struggling to get out of their own half Ireland went close to adding a second when Jonathan Walters arrowed a fine header towards goal, only to be thwarted by Rajkovic.
At the other end, Randolph was fortunate not to concede on the stroke of half-time when he parried a cross to the feet of Aleksandar Mitrovic, but the Newcastle United striker did not react quickly enough to level the scores.
Ireland looked brighter after the break but endured a scare when Antonio Rukavina flashed a shot just wide from the edge of the box and shortly after Serbia drew level.
Tadic, who caused Ireland's defence problems throughout, received the ball in the penalty area and flicked it over the head of John O'Shea before presenting Kostic with a simple finish from close range.
Randolph fought to keep Ireland in the game with a good double save from Tadic, but the Southampton man made no mistake in making it 2-1 from the penalty spot after Jonathan Walters brought down Kostic.
It should have been 3-1 when Randolph dropped Filip Mladenovic's shot at the feet of Andrija Pavlovic, but the substitute could only hit the crossbar despite having an empty net to aim at.
James McClean then headed over the crossbar before Rajkovic parried a Long attempt out for a corner, but the ensuing dead ball was whipped in by Brady and clinically headed in by the unmarked Murphy to send Ireland home relieved to have salvaged a point from a game that looked to be slipping away from them.