How Do you push Against a Team with Superior Waveclear/Stallers?

I have played so many games where we win early and mid game in kills, but we lose the game in the end because if even if we kill like 3 of their team, the remnants split-push/destroy our minions faster than we can destroy theirs making it difficult to take towers. By the time we get a lead, they catch up in items and proceed to lose the game afterwards due to their superior pushing. How does a team win against these comps? It infuriates me to no end to lose a game after 15 minutes of stalemating and hiding.