It most definitely is a save. The criteria for what is considered a save has been around for a long time...
In baseball statistics, the term save is used to indicate the successful maintenance of a lead by a relief pitcher, usually the closer, until the end of the game. A save is a statistic credited to a relief pitcher, as set forth in Rule 10.19 of the Official Rules of Major League Baseball. That rule states the official scorer shall credit a pitcher with a save when such pitcher meets all four of the following conditions[3]:
He is the finishing pitcher in a game won by his team;
He is not the winning pitcher;
He is credited with at least ⅓ of an inning pitched; and
He satisfies one of the following conditions:
He enters the game with a lead of no more than three runs and pitches for at least one inning
He enters the game, regardless of the count, with the potential tying run either on base, at bat or on deck
He pitches for at least three innings