Top seed Djokovic went through a hard first set before found his rhythm back in the second as he best Argentine Juan Monaco 7-5, 6-2.
“Between 4-1 and 4-5 were four quite bad games for me,” he said.
Djokovic will meet Belgian qualifier David Goffin in the next round, who defeated Canada’s Vasek Pospisil 7-5, 1-6, 7-6 (8/6).
Second-seed Murray upset Russian Mikhail Youzhny with a resounding 6-2, 6-3.
Murray needed just 70 minutes to see off his Russian opponent and move into a match with Julien Benneteau of France.
“I put a lot of pressure on myself to get through this one,” Murray said. “With the US Open only a couple of weeks away, I need to stay in form.”
Murray has won the Cincinnati event twice in 2008 and 2011.
Argentine seventh-seed Juan Martin del Potro put out Nikolay Davydenko 7-5, 7-5 while American John Isner beat French eighth-seed Richard Gasquet 7-6 (8/6), 6-2.
Women’s top seed Serena Williams came from one set down to beat Canada’s Eugenie Bouchard before winning 4-6, 6-2, 6-2.