Thursday's contest eclipsed the record of the 15 innings played by Cleveland and Detroit to start the season in 1960.
The Blue Jays rallied to tie it with a three-run ninth and then won it when Arencibia crushed a long homer to left off Jairo Asencio.
Brett Lawrie opened the 16th with a walk and Omar Vizquel put down a bunt. Both runners were safe when Asencio threw wildly to second trying to get Lawrie.
Arencibia's homer came on a 1-2 pitch after he had tried and failed to sacrifice the runners along.
The Blue Jays trailed 4-1 through eight innings, but put their first two batters on in the ninth and scored a run on Jose Bautista's sacrifice fly. Edwin Encarnacion then came through with a one-out, two-run double that tied the contest.
Luis Perez, Toronto's seventh pitcher, worked four hitless innings to get the win. Cleveland did not score over the final 14 innings after Jack Hannahan hit a three-run homer during a four-run second.