Glen Johnson fired Liverpool ahead with the best goal of the match in the 11th minute, before a Mark Noble penalty and an own goal by Steven Gerrard allowed the Hammers to reach half-time 2-1 in front.
But with 14 minutes remaining, substitute Joe Cole levelled matters with James Collins netting the second own goal of the contest on 79 to hand the Merseysiders three points.
The visitors even managed to win without their leading striker Luis Suarez who had to sit out a one-game ban.
But Rodgers said of Shelvey: "He was outstanding. But you see there are two different ways in which you can play the number nine role.
"In this country it is always a very traditional target man, a clear number nine. Give credit to Carlton Cole, I know him form my time at Chelsea, he is a real handful and was outstanding today.
"But you see young Jonjo at 20 years of age playing the number nine role in a different way - dropping into midfield and combining with the midfield players to make the fourth man, being a threat when he is in and around the box, showing great feet and I thought he was outstanding today the kid.
"It was great credit to him because there was a lot of pressure on him because people have been trying to compare him to Luis Suarez.
"But he is only 20 and has a big future ahead of him."