A mainstream pop group had a No.1 US Billboard hit (UK No.5) in 1981 with a hip-hop informed single. That's cultural penetration.
Sugarhill Gang's 'Rapper's Delight' was #3 in the UK in 1979.
You can look up Grand Master Flash, Rock Steady Crew, Run DMC, Adam And The Ants, Malcolm McLarren, Art Of Noise, LOL. It was everywhere. Maybe tate knows better than I do what the actual chart placings were but I know I was immersed in the stuff at the time and as a 10-15 year old not really all that deep into the underground.
Edit: Beastie Boys, LL Cool J....