A team has finished a game with 19-1 singles and extra-base hits 23 times since 1897, most recently Minnesota Twins on 17 June 2012. That is about one every 19,261 team-games.
Box score for the most recent one ↗
18-6 18-7 18-8 18-9 18-10 19-0 19-1 19-2 19-3 19-4 19-5 19-6 19-7
The whole distribution — Singles and Extra-Base Hits · All 18 shapes