Michael Beasley, the second overall draft pick in June, scored 21 points for the Heat but missed a chance to force a second overtime when he the second of his two free throws rattled out in the closing seconds.
The Heat led 41-29 in the second quarter, but the Nets rallied to take an 87-77 lead with less than five minutes left in regulation. Miami fought back before Stromile Swift's dunk put the Nets ahead 91-89 with 30 seconds remaining. Miami's Daequan Cook scored to send the game to overtime.
The Heat play the Nets again on Sunday in London, part of the annual NBA Europe Live tour. Also, the New Orleans Hornets face the Washington Wizards in Berlin on Tuesday, and three days later in Barcelona, Spain.