It was the American’s first match since her fourth round Australian Open exit at the hands of Ana Ivanovic.
Williams fended off two set points en route to taking an opening set tie-break but found life far more comfortable in the second set as she raced through to win 7-6(8) 6-0.
"Today was really difficult for me," said Williams. "I felt so rusty out there and a little frustrated - I've been practicing, but I was like, 'Gosh, this isn't what I practiced,'
"But I was just really excited to get through that. I was really telling myself to stay positive, because I was making a lot of unforced errors that I don't normally make, and my serve wasn't popping the way it usually does."
The Serb edged a final set tie-break to win 3-6 6-3 7-6(6), with Cornet claiming victory after Halep retired with an Achilles injury when a set behind.
Fifth seed Jelena Jankovic was forced to battle back from a break down in each set as she edged Ukranian qualifier Maryna Zanevska 6-4 6-3, while eighth seed Caroline Wozniacki shrugged off the loss of the opening set to beat Wimbledon finalist Sabine Lisicki 2-6 6-3 6-3.
"I think one of my biggest strengths is that I never give up," said Wozniacki.
"I think that's one of the reasons why I've made it so far in my career as well as back in the day, as they say. I think I've won a lot of matches in the past that I probably should have lost."
Dubai Championships results
1-Serena Williams (US) beat Ekaterina Makarova (Russia) 7-6(8) 6-0
Kirsten Flipkens (Belgium) beat Karolina Pliskova (Czech Republic) 6-1 7-5
Flavia Pennetta (Italy) beat Kaia Kanepi (Estonia) 7-5 6-4
Annika Beck (Germany) beat Samantha Stosur (Australia) 1-6 6-1 6-4
Alize Cornet (France) beat 7-Simona Halep (Romania) 6-1 1-1 (Halep retired)
Rio de Janeiro Open results
Patricia Mayr-Achleitner (Austria) beat Yaroslava Shvedova (Kazakhstan) 6-4 6-3
Veronica Cepede Royg (Paraguay) beat Paula Goncalves (Brazil) 7-5 7-6(8)
Teliana Pereira (Brazil) beat 4-Alexandra Cadantu (Romania) 6-3 6-4
Irina Begu (Romania) beat 8-Vania King (U.S.) 6-4 6-0
Lourdes Dominguez Lino (Spain) beat 2-Francesca Schiavone (Italy) 6-4 6-4
Dinah Pfizenmaier (Germany) beat 7-Barbora Zahlavova Strycova (Czech Republic) 2-6 6-4 6-3
Chanelle Scheepers (South Africa) beat Timea Babos (Hungary) 2-6 6-3 6-2
1-Klara Zakopalova (Czech Republic) beat Mariana Duque (Colombia) 6-4 6-4