Only 14.2 overs of play were possible in the opening session, which was interrupted by rain three times.
Chris Rogers is seven not out off 31 deliveries with Shane Watson on 10 from 23 balls.
Australia's skipper Michael Clarke won the toss in overcast conditions and declared the wicket looked outstanding, while rival captain Alastair Cook said the pitch was very dry.
Warner hit four boundaries in an aggressive knock of 29 off 32 balls.
The left-hander fell in a soft manner, silencing the expectant crowd by popping a simple catch to Michael Carberry off a short ball from Stuart Broad with the score on 34.
It's a wasted opportunity for Warner, who hit 49 and 124 in last month's first Ashes Test in Brisbane.
Adelaide Oval's first drop-pitch for a Test match appears brown and flat and has been labelled a road by commentators.
"It's completely lifeless, this pitch," ABC Radio's Jonathan Agnew said.
England have recalled spinner Monty Panesar for his first Ashes Test since 2009 and gambled on 22-year-old debutant allrounder Ben Stokes.
Left-armer Panesar will form a twin-spin attack with offspinner Graeme Swann.
Australia, who lead the five-match series 1-0, named an unchanged line-up with James Faulkner as 12th man.
AUSTRALIA FIRST INNINGS
C ROGERS not out 7 (31)
D WARNER c Carberry b Broad 29 (32)
S WATSON not out 10 (23)
One wicket for 46
Fall: 34 (Warner).
Bowling: J Anderson 7.2-2-20-0, S Broad 6-1-26-1, G Swann 1-1-0-0.
Batting time: 65 mins. Overs: 14.2.
Umpires: Marais Erasmus (RSA), Kumar Dharmasena (SRL).
Match Referee: Jeff Crowe (NZL).
Third Umpire: Tony Hill (NZL).