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The left-hander's unbeaten knock of 116 has helped his side prosper on the opening day of the County Championship match against Leicestershire at the Fischer County Ground.
Worcestershire was 348 for four at stumps. Rutherford's hundred featured 17 fours, and he brought up the milestone from 182 balls.
He is the 10th Worcestershire player to score a century on his red ball debut for the County.
Fellow New Zealander Martin Guptill also achieved the feat in 2018.
Rutherford has signed with Worcestershire on a short-term contract. The 29-year-old, who scored a 171 against England on test debut, will be with the side for the opening month of the 2019 campaign.
He will play in one County Championship match and five one-day games.
Early next month Rutherford will link up with a New Zealand team which will play an Australian XI in three Cricket World Cup warm-up matches.
Wicketkeeper Tom Latham will captain the New Zealand XI.
He is one of just five members of the Black Caps World Cup squad who will feature in the games in Brisbane.
Most of the leading players are unavailable because of Indian Premier League or English county commitments.
Other Otago players are also heading to the United Kingdom this winter. Top order batsman Josh Tasman-Jones will play for Bristol Cricket Club, seamer Matt Bacon is joining Alton and all-rounder Nathan Smith is linking up with Radlett.
Otago co-captain Jacob Duffy is returning to Bishopston. He had a stint there in 2017.
White Ferns and Otago Sparks batsman Suzie Bates is reported to be heading to India for some twenty20 exhibition matches during the Indian Premier League playoffs next month, while Leigh Kasperek is also understood to be United Kingdom bound to ply her trade.
Much improved batsman Polly Inglis is joining Nottingham for her first overseas gig.
New Zealand XI
To play Australian XI
Tom Latham (capt), Hamish Rutherford, George Worker, Henry Nicholls, Will Young, Daryl Mitchell, Jimmy Neesham, Tom Blundell, Doug Bracewell, Todd Astle, Matt Henry, Hamish Bennett, Blair Tickner.