Shaw went 2-for-2 with a double, an RBI and a run scored in Thursday's spring training game against the Twins.
Shaw was 0-for-17 before coming off the bench for a fifth-inning single and eighth-inning double. The 31-year-old, who is a non-roster invitee, is the lone player in camp with extensive history at first base other than starter Bobby Dalbec. That appears to give him a decent chance to break camp on the MLB roster, but Shaw can opt out of his minor-league deal if he's not added to the 40-man roster by Saturday.