Leicester Tigers winger Tuilagi, the leading try-scorer in last season’s Aviva Premiership, opened his account for the tournament after 17 minutes, collecting a smart pass from George Stowers to race over from 22 metres out.
Tuilagi then displayed his trademark power for the second try, holding off three tackles to score in the same corner.
Tuilagi had another score ruled out for a forward pass before collecting his hat-trick try in the second half, rounding off a flowing move that began inside the Samoa half.
Samoa face Wales in their next Pool D game in Hamilton on Sunday.
Ireland, meanwhile, will take on Australia in Auckland without Tigers captain Geordan Murphy. Rob Kearney has been selected at full-back for Saturday’s game.