Gogic and new Scotland call-up Lennon Miller menaced in either box before the interval, but the second half delivered fewer opportunities and more chaos.
Boyd-Munce was carried off after a sickening aerial clash. Ellery Balcombe wiped out team-mate Liam Gordon and Olusanya as he raced out to clear.
Slattery, however, provided another telling moment.
Latching on to a ricocheted Tony Watt knockdown, he flashed, first time, low into the net from 18 yards.
Olusanya continued to career around the Motherwell half and, already on a yellow card, he thundered into Dan Casey. Referee Grant Irvine brandished another.
In a chaotic endgame, 14 minutes of additional time were played, but Motherwell could not stun their depleted guests.
Gogic had the best opening in the dying embers, arrowing a header into the Davie Cooper Stand from a corner.
Slattery's goals keep Motherwell three points clear of St Mirren, though they fall one behind sixth-placed Hearts in the quest to reach the top half.