The University of Chicago's librarians, when the topic came up, could find no trace of a "Dr Blaslotto".
From the outset the Suggestions Office thought this story a little fishy. (A U of C faculty member who's also a world-class powerlifter?) Indeed, trolling through PubMed, Web of Science, and WorldCat revealed no articles or books by Dr. Blaslotto -- leaving us doubtful he even existed.
(another variation of this story adds the claim that he's a world-class powerlifter)
Peculiarly for a world-class powerlifter or a researcher, there seems to be no mention of a Dr Blaslotto on Google except in this story. There are no results for Judd Blaslotto or Dr. Blaslotto on Google Scholar. It does appear that Dr Blaslotto and his study are about as real as the hoops that his second group dunked.
On the other hand, the University of Chicago's librarians do point out another study, from 1960, which does exist, with similar results:
The effect of mental practice was compared with that of physical practice in the development of a motor skill, the Pacific Coast 1-hand foul shot. 144 high school boys were equated into physical and mental practice groups on the basis of arm strength; intelligence; and varsity, junior varsity, or novice experience. Mental practice was found to be nearly as effective as physical practice under the conditions of the experiment.
A 1994 meta-analysis of 35 studies found that mental practise was effective, but not as good as physical practise:
First, the results of this analysis indicate that mental practice is an effective means for enhancing performance. However, the data also indicate that mental practice is less effective than overt, physical practice.
And also dropped off faster:
A 1995 study found that adding mental practise into firearm training for police recruits was effective:
The treatment group mean marksmanship gain score was 32.86 points above the control group's score.
Interestingly enough, they also found that recruits who believed that mental practise would help benefited the most from it (possibly because the worked harder at it).
So, it looks like mental practise does improve performance, though not as much as physical practise. However, it can be combined with physical practise (this may be of particular benefit where resources for physical practise are limited). However, the study cited in the original post appears to have been invented.