Sock, who reached the quarterfinals of last year's tournament, advanced with a 7-5, 1-6, 7-6 (5) victory over France's Adrian Mannarino.
Baghdatis won his first match of the year in three tries by defeating American qualifier Rajeev Ram.
Japan's Kei Nishikori, ranked 16th in the world, is the top seed in the tournament and will play his first match Wednesday. He received a first-round bye.
The 21-year-old Sock defeated Mannarino for the second time this year -- Sock won in straight sets last month in Auckland -- and struggled throughout.
Sock served for the match at 5-3 in the third set, but was broken. In the tiebreaker, he took advantage of a Mannarino backhand error to go up 6-5 and won the match when Mannarino softly netted a second-serve return.
"I just used my scrappiness and my legs," Sock said. "He's a tricky player. He's unorthodox. He hits it hard and flat."
Baghdatis, a top 10 player in 2006, won in straight sets.
"Today I played pretty solid and I'm happy I won," Baghdatis said. "That's all that matters at the end of the day."