The hosts, who won the treble in 2015, could not initially break through a resolute Warrington, who led 6-0 at half-time with Chris Sandow's try.
Brad Singleton and Ryan Hall crossed to put Leeds in front after half-time.
Kevin Penny's converted score gave Warrington a two-point lead and Zak Hardaker failed with a 30-metre penalty which would have earned Leeds a draw.
Leeds 10-12 Warrington as it happened
In their first competitive match since the departures of veteran trio Kevin Sinfield, Jamie Peacock and Kylie Leuluai, Leeds lost captain Danny McGuire to injury just before half-time.
Youngster Jordan Lilley stepped into a half-back position to good effect, producing the pass that sent Hall over, giving the home side a 10-6 advantage.
But at no time was Sinfield's absence felt more than four minutes from time, when last year's Man of Steel Hardaker was unable to land a kick that would have ensured a share of the spoils in the season's opening match.
Warrington finished sixth at the end of a disappointing 2015 campaign, but the performances of half-back pairing Sandow and new recruit Kurt Gidley - as well as their powerful forward pack - pointed to encouraging times ahead for Tony Smith's side.
Ex-Great Britain coach Brian Noble on BBC Radio 5 live sports extra:
"They've set a high standard, both of these teams.
"Leeds were hindered a little with the loss of McGuire, but no excuses. Warrington found enough quality in their attack and we saw some sublime touches from Sandow.
"Leeds were dead and buried at one point, so the win comes down to how well Warrington defended, especially in the scramble moments when Leeds thought they were getting over the line."
Leeds Rhinos: Hardaker; Briscoe, Watkins, Moon, Hall; Sutcliffe, McGuire; Galloway, Burrow, Cuthbertson, Ferres, Ablett, Delaney.
Replacements: Singleton, Garbutt, Keinhorst, Lilley.
Warrington Wolves: Russell; Lineham, Evans, Currie, Penny; Gidley, Sandow; Hill, Clark, Sims, Hughes, Westwood, Westerman.
Replacements: Dwyer, King, Jullien, Cox.
Referee: James Child
Attendance: 16,168
Leeds Rhinos began the defence of their Super League title with a narrow defeat by Warrington Wolves at Headingley.