I think the answer you are looking for is TCP,
HTTP is a protocol that relies on TCP to establish connection between the Client and the Host
In HTTP/1.0 a different TCP connection is created for each request/response pair,
HTTP/1.1 introduced pipelining, wich allowed mutiple request/response pair, to reuse a single TCP connection, to boost performance (Didnt work very well)
So the request and the corresponding response are linked by the TCP connection they rely on,
It's then easy to associate a specific request with the response it produced,
PS: HTTP is not bound to use TCP forever, for example google is experimenting with other transport protocols like QUIC, that might end up being more efficient than TCP for the needs of HTTP