Newcastle saw skipper Fabricio Coloccini sent off in first-half injury time for a professional foul just seconds after Sunderland midfielder Lee Cattermole appeared to get away with two offences inside his own box.
Adam Johnson calmly converted from the spot to give the hosts the lead with their only meaningful attempt on goal to pave the way for a record sixth successive derby win.
Magpies manager Steve McClaren, who had seen his side dominate until Coloccini’s exit, angrily confronted referee Robert Madley on the pitch at half-time but it was to no avail as his hopes of back-to-back league victories went up in smoke, with owner Mike Ashley among a crowd of 47,653 at the Stadium of Light.
McClaren said afterwards: “We are devastated for the fans, for the result and feel very, very harshly done to.”
Fletcher saw a rasping 64th-minute effort deflected just over, but Sunderland extended their lead from the resulting corner when Yann M’Vila’s volley was stabbed into the net by full-back Billy Jones.
Johnson was denied a second goal for the afternoon by the crossbar with 18 minutes remaining, but Fletcher rounded things off with a sweet 86th-minute volley from Younes Kaboul’s pinpoint cross at the end of a pacy counter-attack.
“We were a little fortunate with the first goal but you get these things in the game of football,” said Allardyce.