The Gunners, still reeling from last weekend's 5-1 Premier League loss at Liverpool, twice scored in the opening 50 minutes despite being second best before surviving a second-half onslaught to set up a home quarter-final with Everton.
Arsene Wenger was described as "a specialist in failure" by Chelsea's Jose Mourinho on Friday after last leading Arsenal to a trophy almost nine years ago, in the 2005 FA Cup, but now his side are in the last eight. The Blues are out.
Traore, who joined in January from Monaco, scored after just four minutes but it was his second-half replacement who secured the 3-1 win and safe passage into the quarter-finals.
The Scotland international scored within four minutes of coming on to restore Everton's lead after Jonathan de Guzman's equaliser and won the penalty which Leighton Baines converted.
Toffees manager Roberto Martinez, facing the club over whom he had such an influence between 2007 and 2009, remains on course to complete his quest of becoming the first manager to retain the cup with different clubs, having lifted it with Wigan last May.
Although deep in a relegation scrap in the third tier United have been a different creature in the cup, knocking out Aston Villa and Fulham before adding Forest to the list with a remarkable comeback.
The Blades, comfortably the lowest-ranked team left in the draw, trailed to Jamie Paterson's first-half header until the 68th minute when a goalkeeping howler by Dorus De Vries allowed Conor Coady to tap into an open net.
Then Porter arrived as an 87th minute substitute and produced some authentic cup magic as he converted a last-minute penalty before prodding home again in injury-time.
The result raises the tantalising prospect of a clash with Sheffield Wednesday - should the Owls see off Charlton in their own rearranged fifth-round clash.