Guptill's knock was the core of his side's tally of 89-2 at stumps, the visitors leading by 59 runs after Worcestershire declared at 291-7 in response to New Zealand's first innings score of 261-9 declared.
After making 35 in his first innings, Guptill is putting his name forward for one of the opening slots to take on England in the upcoming test series, with fellow contenders Tom Latham and Hamish Rutherford failing to capitalise on their opportunities overnight.
Rutherford, who top-scored in the first innings with 75, made just eight before being bowled by England all-rounder Moeen Ali, while Latham followed his first-innings seven by being caught at leg slip for just three in his second dig.
The New Zealanders had a mixed day with the ball, starting brilliantly with Matt Henry and Neil Wagner combining to have the hosts at 92-5.
However, a valiant 103no from Ross Whiteley saw his side through to their first-innings advantage.
Ross Taylor will resume with Guptill overnight on 13no when the final day's play gets under way.
