Pic Special: Newcastle 2 Chelsea 0
Gouffran headed home Yohan Cabaye's free-kick with 68 minutes played before Remy wrapped it up with time running out to hand the Magpies all three points.
And it was exactly what Alan Pardew's side deserved for a resolute first half performance, followed by a positive, attacking second half display.
Chelsea had the better chances in the first half, with John Terry twice going close and Branislav Ivanovic also threatening. However, the hosts held firm and took the game to their opponents in the second half.
After Petr Cech had denied Moussa Sissoko and Loic Remy, Gouffran stole in umarked to break the deadlock at the Gallowgate End, before Remy swept home Vurnon Anita's cut-back to put the result beyond any doubt.
It provided Newcastle with their first win in four matches and a first clean sheet in league action since the end of August.
Images by Club Photographer Serena Taylor and the Press Association.