Curran's teammate Jonny Bairstow barked back at Warner while Jimmy Anderson spoke with the umpire.
The verbals continued as players stormed off to their respective huddles at drinks. Warner later fell to Anderson on 103, while Curran continued to bowl with good pace and hostility.
"Warner getting stuck and England have given him plenty as well ... we have seen plenty of Tom Curran in the UK. He will try things, be in the batsman's face," former England captain Michael Vaughan said on the Nine Network.
England captain Joe Root, speaking on Christmas Day, highlighted Curran's competitive streak as one of the big reasons he was selected to replace injured paceman Craig Overton.
"He's a feisty character," Root said.
"He's a real competitor. He's always in the contest."
It isn't the first time Warner has been dismissed in a test, saved by a no-ball, sledged the bowler then scored a test ton. India quick Varun Aaron gave Warner a send-off after rattling his stumps on 66 at the Adelaide Oval in 2014.
The aggressive opener was able to return serve a minute later when he saw footage on the scoreboard of Aaron overstepping. Warner went on to score 102.
Curran followed in the inglorious footsteps of Ben Stokes, who celebrated his maiden test wicket on debut at Adelaide Oval in 2013 then was jeered by the crowd when the third umpire revealed it was a no-ball.
Warner's eventful innings was the highlight of the opening day, which once again saw Australia take the initiative.
At stumps, the hosts had reached 244-3, with Steve Smith and Shaun Marsh building upon Warner's bullocking beginning, and wrestling the clash back away from England, who felt they were in with a sniff after a flurry of wickets.
Warner's wicket came quickly after the dismissal of Cameron Bancroft for 26, and when Stuart Broad had Usman Khawaja caught behind for 17, Australia were reduced to 160-3.
However, Smith (65) and Marsh (31) saw to any concerns of a collapse.
Smith, who hasn't been dismissed at the MCG in a test since 2014, continued his world-leading form, striking six fours as he once more calmly dealt with everything England's bowlers threw at him. Meanwhile, Marsh continued a pivotal Ashes series, with the once under-fire batsman consolidating his current form with a patient knock.
- AAP