Norris beats Verstappen to go fastest in first Australian practice
The Briton Norris powered round the Albert Park circuit with a best time of one minute 18.564 seconds on soft tyres.
He grabbed the lead midway through the hour-long session from Red Bull's Verstappen, who responded with a lightning final lap to be 0.018 adrift.
Verstappen won the first two races of the season in Bahrain and Saudi Arabia, but they were overshadowed by turmoil within the Red Bull camp.
The 26-year-old vowed on Thursday to see out his contract until 2028 and is hoping to put off-track distractions behind him with records on the line at Sunday's Australian Grand Prix.
Verstappen is chasing a 10th consecutive victory to match his own record set last year, while Red Bull are attempting to score a third straight 1-2 finish for the first time in the team's history.
Mercedes' George Russell was third ahead of Ferrari's Charles Leclerc, with RB driver Yuki Tsunoda a surprise fifth.
Sergio Perez in the other Red Bull was sixth and Lance Stroll in an Aston Martin behind him.
Ferrari's Carlos Sainz came eighth ahead of Mercedes' Lewis Hamilton.
It was the Spaniard's first drive since surgery for appendicitis two weeks ago, which forced him to miss Saudi Arabia.
Sainz said he would see how he felt after putting his body through practice before deciding whether to race.
On a perfect autumn day, Hamilton was among the first out and the early pace-setter on medium tyres.
But he complained about "a long brake pedal" on the radio and his time was quickly surpassed with Perez the first under 1:20.
The times continued to tumble with Verstappen assuming the lead on his eighth lap on softs, four-tenths quicker than anyone else, before being knocked off top spot by Norris.
In an eventful practice that reinforced the dangers of the circuit, Fernando Alonso skidded into the gravel at turn 11 while Russell almost lost control at turn 10.
Valtteri Bottas spun his Sauber, also at turn 10, before Albon smashed into the wall at turn 8 in his Williams.
It caused heavy damage on the right side of his car at the front and rear, leaving debris littering the track. Albon said on the team radio "I'm ok" and climbed out, seemingly uninjured.
The session resumed with nine minutes left, but no one could top Norris.
