Watson, 20, won 2-6 6-3 6-2 on Court 13 to set up a meeting with either 32nd seed Mona Barthel or Ksenia Pervak in round two.
The British number one, ranked 50th in the world, bounced back after a medical time-out in which both players received attention.
An elbow injury caused Watson to withdraw from the warm-up tournament in Hobart, but the heat in Melbourne also seemed to be affecting her. She ate some bananas and used some energy gel to get herself right.
"It (the time-out) did help me," she said. "It gave me time to eat, get some fuel in me and just get recharged and motivated. At the beginning I definitely wasn't there, I wasn't playing well.
"I didn't have much energy today, I don't know what it was. I am going to see the doctor after."
Upon the resumption Watson began to cramp up, with the result that she started going for her shots in order to avoid long rallies - and suddenly found her range.
"I knew I couldn't move," she added. "I couldn't be too tense so I just loosened up on everything and just hit it. I'm just so glad that I did cramp."
Romanian Cadantu must have fancied her chances when Watson's opening second serve of the match hit the foot of the net.
And at a set and 3-1 up in a low-quality encounter, the world No.91 looked odds-on to reach round two. However the medical break during game five gave Watson a fresh start: she went on to hold then reeled off another three straight games.
Watson went a break up in the decider but Cadantu, despite struggling with her arm and foot, managed to break back. However she was unable to continue that brief momentum and Watson raced to victory to reach the second round in Melbourne for the first time.
Her fellow Briton Laura Robson faces American Melanie Oudin on Tuesday.
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