Australia fast bowler Mitchell Starc has been ruled out of the fourth Ashes Test against England with a heel injury, with Jackson Bird named as his replacement.
Warner, who had been marooned in the 90s for over 40 minutes, looked poised on 99 to bring up his century as he faced the last ball of debutant Tom Curran's fifth over.
Warner didn't stay at the crease for much longer after his let-off, as he was caught behind off James Anderson for 103.
Bancroft shared in a 122-run opening stand and was the passive partner as Warner chased runs.
Woakes removed Bancroft leg before for 26 early in the session, the tourists' first reward following a fruitless morning after Smith won the toss and opted to bat.More news: Tunisia bans Emirates Airlines flights
Cricket Australia confirmed before Sunday's team practice session that he would miss the match in Melbourne - which starts on Tuesday - with fellow quick Bird coming in. Or will England finally fire a shot?
Warner faced 151 balls and hit 13 fours and a six off Moeen Ali in the over before lunch.
He celebrated with his customary leap and fist-pump but Anderson mercifully cut short Curran's agony with a fine delivery that jagged back off the seam to catch the edge on the way through to wicketkeeper Jonny Bairstow.
Australia have already regained the Ashes after they won the third match in Perth at the WACA to give them an unassailable 3-0 lead in the five-match series.
England paceman Tom Curran is debuting in the absence of injured team-mate Craig Overton, who has a cracked rib.