England reached the round of 16 while the Slovenes were knocked out of the tournament.
Jermain Defoe turned home James Milner's cross from five meters with a right-foot volley in the 23rd minute to give England five points in the group. Slovenia finished with four but failed to advance because the United States beat Algeria 1-0 and won the group.
Showing much better form after its dismal 0-0 draw with Algeria, when the team was booed off the field, England created several more chances throughout the match.
"This team, this spirit, played together and tried together," England coach Fabio Capello said. "I am really happy because I found the team I know. We now go forward.
We can play against all the teams because the mind is now free." For the first 10 minutes, England again looked nervous, but the players then began to produce some flowing moves and the chances followed.
"It's been difficult for the supporters because they weren't happy with the performances," Defoe said. "A lot of the top teams have struggled so it was important to keep the spirit, which we have done."
Frank Lampard, Wayne Rooney and Glen Johnson all had goalbound shots. On the other end, goalkeeper David James had to react sharply to keep out a flick-on from Slovenia defender Bostjan Cesar.
England continued to dominate after the goal and Slovenia goalkeeper Samir Handanovic had to make two saves within a few seconds of each other to keep out shots from Defoe and Steven Gerrard.
Blunders in the Slovenia defense handed Defoe a second chance in the opening minute of the second half, but he flicked the ball wide from Gareth Barry's headed pass.
England continued to create chances after that and Handanovic blocked John Terry's powerful header at the near post and then finger-tipped Rooney's shot onto the post.
Slovenia almost equalized in the 68th after Barry lost possession and Terry and Johnson blocked goalbound shots from Zlatko Dedic and Milivoje Novakovic.
Samir Handanovic, Miso Brecko, Marko Suler, Bostjan Cesar, Bojan Jokic, Robert Koren, Andraz Kirm (Tim Matavz, 79), Aleksander Radosavljevic, Valter Birsa, Zlatan Ljubijankic (Zlatko Dedic, 62), Milivoje Novakovic.
David James, Glen Johnson, John Terry, Matthew Upson, Ashley Cole, James Milner, Gareth Barry, Frank Lampard, Steven Gerrard, Wayne Rooney (Joe Cole, 72), Jermain Defoe (Emile Heskey, 86).
