The 12th-ranked Berdych's third break of Johansson's serve gave him a 6-5 lead in the second set, and he wrapped up the match in 1 hour, 17 minutes at the grass-court event, a key tuneup for Wimbledon.
Berdych took the crown last year with Roger Federer absent, following four straight years in which the world's No. 1 player had won the event en route to his Wimbledon titles. Two years ago, Berdych was defeated in the final by Federer.
Federer plays his first match of the tournament Wednesday against 89th-ranked Michael Berrer and will be seeking to extend his record 54-match winning streak on grass that dates to 2002.