A team has finished a game with 13-10 singles and extra-base hits 10 times since 1897, most recently Boston Red Sox on 9 July 2008. That is about one every 44,300 team-games.
Box score for the most recent one ↗
13-4 13-5 13-6 13-7 13-8 13-9 13-10 13-11 13-12 13-13 13-14 13-15 14-0
The whole distribution — Singles and Extra-Base Hits · All 18 shapes