Zech Medley twice put Arsenal in front at Meadow Park, only for Monaco to equalise each time during the first half.
After the break Monaco went ahead but Balogun's penalty levelled the tie, before the visitors had Enzo Millot sent off with five minutes remaining.
In the third minute of added time, Balogun made Arsenal's man advantage count to score and send the Gunners through as the first team to reach the last four.
See: Arsenal report
Tuesday 10 March
19:00 Derby County v West Ham
19:00 Liverpool v Wolfsburg
Wednesday 11 March
19:00 Swansea v Benfica