A team has finished a game with 18-1 singles and extra-base hits 23 times since 1897, most recently Minnesota Twins on 31 July 2003. That is about one every 19,261 team-games.
Box score for the most recent one ↗
17-8 17-9 17-10 17-11 17-12 18-0 18-1 18-2 18-3 18-4 18-5 18-6 18-7
The whole distribution — Singles and Extra-Base Hits · All 18 shapes