Warner, who scored a century in Australia's huge 381-run win in the series opener in Brisbane, set off at a cracking pace in Adelaide after Michael Clarke won the toss and chose to take first advantage of the drop-in pitch.
The 27-year-old struck 29 off 32 balls with four fours before he went after a wide Broad delivery and was caught by Michael Carberry at point in the eighth over, leaving the home side 34 for one.
Australia were 46 for one when an early lunch was taken after the third rain interruption of the morning session.
Chris Rogers, looking for a confidence-boosting innings after two failures at the Gabba, was not out seven off 31 balls with Shane Watson on 10.
Broad, who took eight wickets in the opening Brisbane Test, had figures of one for 26 off six overs.
England captain Alastair Cook introduced spinner Graeme Swann into the attack in the 14th over of the innings.
The tourists made two changes following the departure of batsman Jonathan Trott with a stress-related illness.
Joe Root was elevated to Trott's spot at first wicket down and England gave Durham allrounder Ben Stokes his first Test cap, presented to him by former captain Andrew Strauss before play.
Monty Panesar was also included in a twin-spin attack with Swann on a dry pitch expected to take turn later in the match.
Australia named an unchanged side, with James Faulkner again the 12th man.