The 22-year-old opened the scoring for Bologna with a steer header in the 26 minutes of the first half.
Barrow also produced a wonderful assist as he made a strong run from the midfield, riding a couple of tackles before putting a cross for Matias Svanberg to restored their lead in the 41 minutes.
Bologna extended their advantage through Roberto Soriano in the 70 minutes of the second half.
Sampdoria who have a Gambian international (Omar Colley) in their books scored their only consolation goal of the match through Fabio Quagliarella in the 37 minutes after cancelling Musa Barrow’s opener.
Meanwhile, Omar Colley did not feature for Sampdoria during the game due to suspension.
The goal and assist were the sixth league goal and six assists by former Hawks FC player Musa Barrow after 27 matches for Bologna.
The result has left both sides in the bottom half of the table.
Bologna now sits twelfth position with 31 points, whiles Sampdoria are one point ahead with 32 points on eleventh position after 27 matches.