Miami - Six-time winner Serena Williams survived a first-set scare before overcoming Yaroslava Shvedova 7-6 (9/7), 6-2 on Thursday to power into the third round of the ATP and WTA Miami Masters.
The top-seeded defending champion will next face France's Caroline Garcia after dispatching her Kazak rival in one hour, 45 minutes.
"The first set was really tough. She can make you play. She was hitting the ball well," Williams said.
"I had to relax and try to keep my intensity and just try to get the win."
Fourth seed Maria Sharapova, the 2013 runner-up to Williams, outlasted Japan's Kurumi Nara 6-3, 6-4 in another opening test.
Williams lost a 3-1 lead and trailed 3-5 as Shvedova shifted her game up a gear.
Williams got back on track in the nick of time with a break for 5-all. A love game then ended with an ace for Williams before the set went to a tie-breaker.
In the decider, the 32-year-old Williams saved three set points as a nervous Shvedova missed her big upset chance in front of a screaming house full of her rival's supporters.
In one dramatic moment, a fight broke out in the upper deck of spectators, forcing a pause for security to intervene after Shvedova had double-faulted on her second set point.
After she also missed on a third, the Kazak handed over a set point to Williams, who finally finished off the 63-minute set on her second opportunity.
Williams tried to steady the second after a pair of breaks and finally won going away as she aced on her first match point to book a date with Garcia, who beat Czech Klara Zakopalova 7-6 (7/3), 7-6 (7/3).
"I'm just happy for another win," said a relieved Williams, who was playing for the first time in a month while healing back pain.
Sharapova was down 1-3 in the 64-minute second set before rallying to beat Nara, who won her first WTA title in Rio de Janeiro last month.
"She made me work extremely hard," said Sharapova. "She's a really quick opponent, got a lot of balls back, and she made me hit a lot. She made me try to do too much in certain situations.
"Sometimes I felt like I was doing the right mistakes and sometimes I felt like I should have been more patient, but I guess those are the situations you want to build that match confidence again."
Four-time Grand Slam champion Sharapova, who next faces Lucie Safarova, was coming off a third-round loss at Indian Wells to qualifier Camila Giorgi.
"I still feel like a work in progress," Sharapova said. "That match strength, when you're deep into the match and just in the later stages of matches, I think that's the thing that's hurt me in these last couple of months.
"But I've got to work through that. Nothing's just going to come to me. It's a challenge I have ahead of me, and I have to face it."
Australian veteran Lleyton Hewitt captured his 600th career victory while countryman Bernard Tomic became the fastest loser in ATP history.
Former No 1 Hewitt rallied to defeat Dutchman Robin Haase 2-6, 6-3, 6-3 to reach the second round while Tomic fell in his first match since January hip surgery 6-0, 6-1 to Finland's Jarkko Nieminen.
Tomic, ranked 74th, crashed out in 28 minutes, 20 seconds, believed to be the ATP's shortest match by a minute. Tomic was playing for the first time since a retirement against Rafael Nadal in a first-round match at the Australian Open.
Hewitt, 33, turned in another of the trademark fightbacks which have characterised a career that included Grand Slam crowns at Wimbledon in 2002 and the US Open in 2001.
The 44th-ranked Australian reversed course in the second set to reach the second round in just under two hours, with Haase saving a match point before exiting.
"It's not something you focus on, to tell you the truth. I totally forgot," Hewitt said of his 600th triumph.
"Obviously afterwards, it's a great milestone. Not many people get to achieve that. Not many people get the opportunity to get close to that, so it means I've been around for an awfully long time as well. I'm getting old.
"A few years ago when I had the last couple lot of surgeries I probably would have doubted I'd get to this stage anyway. I'm still grateful I'm out there and able to compete with the best guys."
Results on Thursday from the third day of the WTA and ATP Miami Masters (x denotes seeded player):
Jack Sock (USA) bt Guido Pella (ARG) 6-3, 6-4
Denis Istomin (UZB) bt Nicolas Mahut (FRA) 7-6 (10/8), 7-6 (7/2)
Stephane Robert (FRA) bt Alex Bogomolov (RUS) 7-5, 6-4
Aljaz Bedene (SLO) bt Jimmy Wang (TPE) 1-6, 6-2, 6-4
Daniel Gimeno-Traver (ESP) bt Karen Khachanov (RUS) 6-7 (8/10), 6-1, 6-1
Edouard Roger-Vasselin (FRA) bt Igor Sijsling (NED) 3-6, 6-3, 7-6 (7/3)
Lukas Lacko (SVK) bt Kenny De Schepper (FRA) 6-4, 6-4
Lu Yen-Hsun (TPE) bt Mikhail Kukushkin (KAZ) 6-1, 3-1, retired
Ryan Harrison (USA) bt Federico Delbonis (ARG) 6-2, 6-4
Guillermo Garcia-Lopez (ESP) bt Bradley Klahn (USA) 1-6, 6-1, 6-4
Jarkko Nieminen (FIN) bt Bernard Tomic (AUS) 6-0, 6-1
Lleyton Hewitt (AUS) bt Robin Haase (NED) 2-6, 6-3, 6-3
Donald Young (USA) bt Carlos Berlocq (ARG) 6-2, 6-2
Joao Sousa (POR) bt Pablo Carreno Busta (ESP) 6-4, 7-6 (7/3)
Roberto Bautista Agut (ESP) bt Steve Johnson (USA) 4-6, 6-3, 6-1
Sam Querrey (USA) bt Sergiy Stakhovsky (UKR) 7-6 (7/2), 6-3
Angelique Kerber (GER x5) bt Peng Shuai (CHN) 6-3, 1-6, 7-6 (7/5)
Tsvetana Pironkova (BUL) bt Sorana Cirstea (ROM x25) 6-3, 6-3
Ekaterina Makarova (RUS x23) bt Rebecca Peterson (SWE) 6-1, 6-1
Ana Ivanovic (SRB x12) bt Lauren Davis (USA) 6-1, 6-1
Samantha Stosur (AUS x16) bt Kiki Bertens (NED) 6-3, 6-2
Donna Vekic (CRO) bt Svetlana Kuznetsova (RUS x28) 7-6 (7/5), 7-5
Petra Kvitova (CZE x8) bt Paola Ormaechea (ARG) 6-3, 6-4
Sara Errani (ITA x9) bt Patricia Mayr-Achleitner (AUT) 6-1, 6-4
Sabine Lisicki (GER x14) bt Nadia Petrova (RUS) 3-6, 6-4, 6-4
Caroline Garcia (FRA) bt Klara Zakopalova (CZE x27) 7-6 (7/3), 7-6 (7/3)
Flavia Pennetta (ITA) bt Olga Govortsova (BLR) 6-3, 6-3
Lucie Safarova (CZE) bt Vania King (USA) 6-3, 6-3
Kirsten Flipkens (BEL) bt Virginie Razzano (FRA) 6-1, 3-6, 6-3
Serena Williams (USA x1) bt Yaroslava Shvedova (KAZ) 7-6 (9/7), 6-2
Coco Vandeweghe (USA) bt Anastasia Pavlyuchenkova (RUS x21) 7-6 (9/7), 7-5
Maria Sharapova (RUS x4) bt Kurumi Nara (JPN) 6-3, 6-4