Stephens, the 2017 U.S. Open champion, was off court in less than an hour after romping to a 6-0 6-2 win over Yafan Wang which took her into round three for the first time since 2016.
Johnson, however, had to toil for almost 3-1/2 hours under a blazing sun before he was able to crawl past Australian 25th seed Alex de Minaur 3-6 7-6(4) 6-3 3-6 6-3.
Next up for him will be Japan's Kei Nishikori.
The duo are among 11 Americans in action on day four of the championships, with seven-times singles champion Serena Williams headlining the 4th of July billing.
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(Reporting by Pritha Sarkar, editing by Ed Osmond)
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