A team has finished a game with 7-13 singles and extra-base hits 6 times since 1897, most recently Minnesota Twins on 5 July 2019. That is about one every 73,834 team-games.
Box score for the most recent one ↗
7-7 7-8 7-9 7-10 7-11 7-12 7-13 7-14 7-15 8-4 8-5 8-6 8-7
The whole distribution — Singles and Extra-Base Hits · All 18 shapes