A team has finished a game with 19-2 singles and extra-base hits 16 times since 1897, most recently Philadelphia Phillies on 20 September 2012. That is about one every 27,687 team-games.
Box score for the most recent one ↗
18-7 18-8 18-9 18-10 19-0 19-1 19-2 19-3 19-4 19-5 19-6 19-7 19-8
The whole distribution — Singles and Extra-Base Hits · All 18 shapes