The world number one, who had been forced to retire in her last appearance on Tour at the Wuhan Open due to illness, emerged victorious 7-5 6-2 after a superb showing of resiliency.
Qualifier Soler-Espinosa capitalised on a dreadful start from the American to race into a 5-0 lead and looked set to condemn the US Open champion to a rare bagel, only for Williams to fight back and save three set points to finally get on the board.
Williams then denied her opponent on a further set point in the next game and proved unstoppable from there as she won seven straight games to take the set.
By that point Soler-Espinosa's fight had all but disappeared, allowing Williams to wrap up the victory in comfortable fashion and set up a second-round meeting with Tsvetana Pironkova after the Bulgarian beat Maria Kirilenko 6-4 6-1.
There was to be a slight first-round surprise on Monday, however, as France's Alize Cornet – the beneficiary of Williams' retirement in Wuhan – knocked out 10th seed Jelena Jankovic in three sets.
Just nine places separate Serbian Jankovic and Cornet in the rankings, and that fact was well demonstrated in a gruelling contest that saw the Frenchwoman prevail 7-5 3-6 6-4 in two hours and 39 minutes after turning around a 2-0 third-set deficit.
However, there were no difficulties for Jankovic’s compatriot Ana Ivanovic, the ninth seed hammering Belinda Bencic of Switzerland 6-2 6-1, while Flavia Pennetta and Lucie Safarova also progressed.
Pennetta overcame Christina McHale 7-6 (7-3) 6-4 but her Italian compatriot Camila Giorgi was beaten by Czech Safarova by an identical scoreline.
The all-Chinese clash at the WTA Premier hard-court event ended in victory for Peng Shuai as she went through in straight sets versus Zhang Kai-lin, although fellow home hope Zhang Shuai saw her challenge ended by Caroline Garcia of France.
Elsewhere in the draw there were wins for Mona Barthel and Lauren Davis.