A team has finished a game with 20-1 singles and extra-base hits 5 times since 1897, most recently Milwaukee Braves on 25 August 1961. That is about one every 88,600 team-games.
Box score for the most recent one ↗
19-7 19-8 19-9 19-10 19-11 20-0 20-1 20-2 20-3 20-4 20-5 20-6 20-7
The whole distribution — Singles and Extra-Base Hits · All 18 shapes