Ezri Konsa's header just before halftime (44') and Ollie Watkins' goals (51' and 90+4') gave Villa hope and put them on track for their first trophy since winning the League Cup 30 years ago.
Difficult challenge heading into the return fixture in Birmingham
Villa will face either Porto or Nottingham Forest in the semi-finals, after the two sides drew 1-1, should they overcome Bologna, who remain in contention thanks to Jonathan Rowe's stunning late goal (90'). The second leg will be played next week in Birmingham. Bologna have won their last seven away matches in all competitions, but Spanish manager Unai Emery has won the Europa League four times, and his Villa side are the favourites to advance.
Aston Villa have beaten Bologna three times in the last two seasons, including twice in this edition of the Europa League, where the English side proved decisive in their victories over the stubborn Bologna side.