A team has finished a game with 18-3 singles and extra-base hits 39 times since 1897, most recently Detroit Tigers on 25 September 2010. That is about one every 11,359 team-games.
Box score for the most recent one ↗
17-10 17-11 17-12 18-0 18-1 18-2 18-3 18-4 18-5 18-6 18-7 18-8 18-9
The whole distribution — Singles and Extra-Base Hits · All 18 shapes