The 27-year-old seamer took five for 45 in 18 overs although he was spoken to by umpire Nigel Cowley for hitting opener Billy Godleman when he tried to throw down the stumps. Wagner finished with eight wickets in the match and although Dan Redfern made 58, Derbyshire never looked like chasing down a target of 335 and were bowled out for 227 after tea.
The tourists declared on their overnight score of 199 for five, which left Derbyshire facing a demanding target based on their first innings when they offered little resistance and were all out for 154, but at least they made a promising start with Chesney Hughes and Godleman putting on 42 for the opening wicket, before Wagner broke through in the 13th over.
He had beaten Hughes several times but when the big Anguillan had made 15, he edged one that moved away to be caught behind by Tom Latham, who kept wicket in the morning session before BJ Watling took over after lunch.
Wagner, who is vying with Doug Bracewell for a place in next week's Lord's Test, again bowled with hostility but he overstepped the mark in his next over when he hurled the ball back at Godleman and knocked the bat out of his hand.
Wagner raised a hand in apology but was spoken to by umpire Cowley, who also had words with acting captain Kane Williamson although the bowler would have the final say. In his next over, he got a full length ball through the opener's defence to trap Godleman plumb in front for 25.
Wes Durston played confidently from the start and was steering Derbyshire towards the lunch interval before Bruce Martin bowled captain Wayne Madsen with one that kept low.
The home side suffered another blow in the third over of the afternoon session when Durston launched into a drive at wide ball from Bracewell and was pouched at second slip by his former team-mate Martin Guptill.
Ross Whitely also fell to a loose shot at Bracewell and at 98 for five, Derbyshire were in danger of going down without a fight, but Redfern responded with some defiant strokes and raced to a 50-ball half-century with three consecutive fours off Mark Gillespie.
But his innings ended tamely when he pushed out at Wagner and was caught behind and the end came shortly after tea to give the tourists a morale boosting victory ahead of this week's game against England Lions at Leicester.