Should this end as it is, the Red Sox would have 9 consecutive wins over the Angels, going back to the last three games of the 86 ALCS, which made me try and think of other long postseason streaks of one team over another.
Off the top of my head I thought of the Yankees winning 9 straight against the Rangers in the late 90s, and the A's winning 10 straight over Boston (88 and 90 ALCS sweeps, first two of 03 DS). I gave a cursory glance at MLB's postseason history and nothing else really stood out to me, but maybe our own statbot knows of some others