The pulsating clash had a dramatic climax as Brighton's Tariq Lamptey was sent off in stoppage time moments before referee Michael Oliver rescinded a penalty he awarded to Villa after a VAR check.
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Sixth-placed Villa's patchy form continued as they suffered their third successive home defeat, the setback against Brighton coming after a 3-0 win at Arsenal following losses to Leeds and Southampton.
Welbeck, who endured a difficult year at relegated Watford last season with only two league goals in 18 appearances, was delighted after opening his account at Brighton.
"We've had some good performances but today we got the result as well. I'm obviously happy to get off the mark with the goal. I just kept my cool and slotted it over the keeper."
Villa missed a string of chances in the first half and were punished as Welbeck raced clear from inside his own half in the 12th minute and beat goalkeeper Emiliano Martinez with a deliciously dinked finish.
Konsa equalised shortly after the break when he slid in at the far post to turn in Bertrand Traore's free kick and Villa looked set to complete their comeback as they kept laying siege to the Brighton goal.
But they were stunned again in the 56th minute when March capped a flowing move with a sublime first-time shot from 18 metres into the top corner, leaving Martinez rooted to his line.
March, whose tackle on Trezeguet was initially seen by Oliver as a penalty, was relieved the referee changed his mind after reviewing the replay of the incident on a monitor.
"For a moment I had my heart in my mouth but I got a bit of the ball," he said to the BBC. "I haven't seen it back but sometimes with the follow-through you cannot avoid making contact."