The Eels, who hadn't won on the road since 2010 when trailing at halftime, fell further behind when Daniel Mortimer's pinpoint kick early in the second term allowed Anthony Don to score.
The game turned, however, when Hayne fended off NSW State of Origin teammate Greg Bird and sprinted 70m to level the scores.
Minutes later, the fullback ran onto a Chris Sandow pass to charge over and give the Eels the lead for the first time with 20 minutes to play.
Sandow, who had a hand in three Eels tries, then grubbered a kick with 11 to go which Mortimer spilled for Corey Norman to gleefully dive onto and seal a crucial win.
A late breakaway by James Roberts gave the Titans hope but time ran out for John Cartwright's men.
The Titans head north next weekend to take on North Queensland while Parramatta are away to Cronulla.