A team has finished a game with 6-3-1 runs-hits-errors line 5 times since 1897, most recently Chicago Cubs on 16 April 1982. That is about one every 88,600 team-games.
Box score for the most recent one ↗
6-1-0 6-2-0 6-2-1 6-2-3 6-2-2 6-3-2 6-3-1 6-3-4 6-3-0 6-3-3 6-4-7 6-4-1 6-4-2
The whole distribution — Runs-Hits-Errors Lines · All 18 shapes