England's international Moeen Ali (20*) was resolute as he carried his bat to the close of play and Worcestershire will resume tomorrow 196 runs behind with nine wickets in hand.
After the opening day of the four day match was washed out by heavy rain, stand-in skipper BJ Watling won the toss and opted to bat in the warm and fine conditions.
The New Zealand XI made a steady start but lost wickets at regular intervals with Tom Latham (7), Guptill (35) and Ross Taylor (12) all departing to be 96-3 after 27 overs.
Guptill, in his comeback match from a side strain and pressing for a spot in the Test side, timed the ball superbly before he was undone by a slower ball from Jack Shantry to be caught at mid-off.
Meanwhile Rutherford, the son of former Black Caps skipper Ken, was the mainstay throughout.
He brought up his half century from 82 deliveries, and then combined with Mark Craig (17) for a 35 run partnership. He was stumped by Ben Cox off the bowling of Ali.
Worcestershire, cheered on by a sizeable crowd at one of England's traditional grounds, bowled with accuracy. Ross Whiteley (2-16), Ali (2-35) and Charlie Morris (2-32) were the best performers as they restricted the New Zealand side.
In the latter stages, Bracewell and Wagner frustrated the Worcestershire attack with the former playing a leading role in the partnership striking six fours and a six in his innings.
His time at the crease came to an end when he was caught behind by Cox from the bowling of Ed Barnard and moments after Watling indicated the declaration from the balcony of the pavilion.
The New Zealand bowling line up, with Matt Henry and Ben Wheeler opening the attack, looked for early wickets but they were met by resistance and will hope to make inroads tomorrow.
This match against Worcestershire is not a first class fixture so the full squads from both teams can be interchanged throughout the match.
FIRST INNINGS: New Zealand XI 261-9d (Rutherford 75, Bracewell 43; Whiteley 2- 16) v Worcestershire 65-1 (Oliver 30, Ali 20*; Wagner 1- 6) at New Road. Worcestershire trail by 196 runs with nine wickets in hand.