Murray underwent hip surgery past year and has since struggled to put injuries behind him as he bids to add to his haul of three Grand Slam titles and 47 career titles in all.
The second set was more one-sided as Murray, a two-time victor of the hard-court tournament which serves as a warm-up for the Australian Open, allowed Medvedev to power 4-0 ahead.
"I think for the first match of the new year after quite a long break, it was alright".
Stephens, the 2017 U.S. Open champion, finished last season in the top 10 for the first time and is more concerned about the Australian Open later this month than recording a loss in her season-opener in Brisbane.
In his latest comeback from a hip injury the two-time Wimbledon champion was beaten 7-5, 6-2 by the fourth seed from Russian Federation, just weeks before the start of the Australian Open.
Murray put up a fight in the first set by taking the tournament fourth seed to a tie break before 14 winners by Medvedev ended his resistance after 47 minutes.
The tournament lost another big name when Rafa Nadal pulled out due to a thigh strain, casting doubt on his participation in this month's Australian Open.
However, after conferring with his doctors he chose to withdraw to ensure he would be fit to play the Australian Open later this month.
In a replay of last year's final, Sasnovich reversed that result as she ousted Svitolina 6-4, 0-6, 6-3. Nishikori opened his year with a 7-5, 6-2 win over Denis Kudla.
Serving for the win at 5-2, Medvedev hit three unreturned serves to seal the deal and march towards the quarter-final where he will face Milos Raonic.
Murray, who didn't appear hampered with his movement, said he could feel his touch returning as the match progressed.
Austria's Dominic Thiem, the No. 2 seed, was surprisingly beaten by the world No. 55, France's Pierre Hugues-Herbert, 6-3, 7-5 in the last match on Tuesday.
He has been replaced in the draw by lucky loser Taro Daniel of Japan, who will play Jo-Wilfried Tsonga on Thursday.
Also in the first round, Ivana Jorovic of Serbia upset second-seeded Caroline Garcia of France, 6-4, 6-2, and Alison Riske of the United States defeated No. 3 Wang Qiang of China, 6-3, 6-3.