Sarkisov had only been on the pitch for six minutes before his close range strike gave the visitors all three points in this Group B encounter at the Ta' Qali National Stadium.
Hogg also had to deny Henrikh Mkhitaryan's strike while Movsisyan's volley cannoned off the post as Vardan Minasyan's men continued to push forward.
Both sides had chances to break the deadlock after the interval but Sarkisov's introduction proved pivotal. The striker, who came on for Marcos Pizelli, slotted home Movsisyan's left-wing cross to give Armenia the lead with Hogg finally beaten.
Hogg was the busier of the two keepers thereafter too, making fine saves from Mkhitaryan and Movsisyan in the closing stages.