The 26-year-old Austrian signed off with a four-day total of 18-under-par 270 to lift his maiden Tour title.
While Jeev totalled five-under 283, Anirban Lahiri (73) was tied 49th at even par 288 and Digvijay Singh (73) was tied 70th. Jeev had three birdies against no bogeys and his birdies came on fifth, ninth and 18th holes.
Second-placed Richie Ramsay of Scotland battled to a flawless 65 but was still not good enough to overtake Wiesberger, who was always in complete control.
France's Victor Dubuisson, who took the opening round lead, grabbed a share of third place alongside 2010 Ballantine's Championship winner, Marcus Fraser of Australia on 277.
Thailand's Kiradech Aphibarnrat and Asian Tour honorary member Y E Yang of Korea were the highest placed Asians after they signed off with 281 to take a share of 15th place alongside England's Ian Poulter, Wales' Jamie Donaldson and David Oh of the United States.
Starting the day with a five-shot lead, Wiesberger reached the turn in 35 after a birdie on the par-five fifth. He continued to par holes 10 to 14 and there was never going to be any question on who will win the Ballantine's Championship once the Austrian birdied the 15th and 16th holes.
Wiesberger's victory at the Blackstone Golf Club was made even sweeter when he signed off with another birdie on the closing par-five 18th. PTI Cor AH