The world number two, who won Wimbledon and an Olympic gold medal in the summer, sealed a 6-2 7-5 victory to kick off his campaign.
Murray put pressure on Seppi's serve early in the first set, but the Italian managed to save three break points to keep himself in contention.
It did not last long, though, as the Scotsman earned a double break to give himself a one-set lead in 34 minutes.
Murray suffered a wobble at the start of the second set as he was broken at the first time of asking, and after breaking back, the three-time Grand Slam winner was kept at bay for the next seven games.
The breakthrough was eventually made by the 29-year-old, who took 53 minutes to wrap up the set.