Billy McKay picked up his goalscoring form of the last two seasons in the 10th minute, lobbing Michael McGovern after a defensive mix-up.
Ryan Christie added a second with 25 minutes on the clock as John Hughes' side looked set for a big win.
Marley Watkins' effort hitting the crossbar was as close as they came to extending their advantage, while Hamilton saw penalty appeals turned away as they tried in vain to get back into the contest.
However, the Lanarkshire club were unable to muster a response and slipped to defeat on their top-flight return.
Motherwell also opened their domestic campaign with a win, atoning for disappointment in the UEFA Europa League by beating St Mirren 1-0.
Stuart McCall had seen his side dumped out of Europe's second-tier competition in the third qualifying round by Iceland's Stjarnan but Lee Erwin stepped up on debut to prod home the winner, while St Mirren had player/coach Jim Goodwin sent off for two bookable offences.
Dundee made their return to the Premiership on Saturday and marked the occasion with a 1-1 draw against Kilmarnock at Dens Park.
Ex-Kilmarnock midfielder Gary Harkins converted a 17th-minute penalty he had won himself to put the hosts ahead, but Craig Slater fired a fine free-kick home to equalise just eight minutes later.
Visiting goalkeeper Craig Samson was called upon several times in the second half, but remained resolute to preserve a point for his side.
There was a moment of note in the Scottish Championship as debutant goalkeeper Mark Oxley scored a freak goal from his own half for Hibernian as they began life in the second tier with a 2-1 win over Livingston.
