Former City forward Lee Geum-Min grabbed a stoppage time consolation for the visitors, but the damage had already been done at the Academy Stadium.
City opened the scoring when a Chloe Kelly corner found its way in at the near post through a combination of Sarri and Brighton stopper Megan Walsh.
Number two followed soon after when Blakstad headed home Kelly's cross for her third goal in as many matches.
An emphatic strike from Coombs ensured the hosts were out of sight by the break, with Deyna Castellanos and Blakstad also going close in the second 45 before Lee Geum-Min's close-range effort late on.
Check out highlights from the encounter via the video above...