Stack raced out to make another save when Hulse got clear of the Gunners defense in the 49th minute and then Lee Hughes fired over the bar with just the 'keeper to beat.
But an amazing blunder by Albion 'keeper Hoult handed the Gunners a second goal in the 56th minute.
A standout player for West Brom for the past three seasons, he collected a backpass and played it straight to Aliadiere who had the simplest job of rolling the ball into an empty net.
There was another injury worry for the officials when referee Matt Messias had to go off for treatment for a calf muscle problem with the second half only 18 minutes old. He was able to resume after two minutes.
Although the Gunners had more of the play after the second goal, Albion, who had 10 corners to Arsenal's none, showed signs of hitting back when Scott Dobie rattled the crossbar six minutes from the end.
Then Hughes climbed to meet a well floated cross from Macedonian midfielder Artim Sakiri only for his header to flash just wide of the near post.
At the Reebok Stadium, Southampton 'keeper Antti Niemi made a series of saves to keep out shots from Jay Jay Okocha, Pedersen and Stelios Giannakopoulos while Wanderers' Bruno N'Gotty and Mario Jardel also missed chances.
After Youri Djorkaeff had a goal ruled out for offside, Niemi was beaten in the 115th minute when Anthony Barness drove in a cross and Pedersen turned the ball home at the far post.
Saints almost equalized when Paul Telfer fired in a shot which Bolton's 40-year-old 'keeper Kevin Poole, in his 19th season as a pro, pushed onto the crossbar.
Italian Cup
Perugia, fired by goals by Christian Obodo, Soulemayne Diamoutene and Jay Bothroyd, reached the quarterfinals of the Italian Cup on a 3-0 home win over Chievo in a third-round, second leg match that improved its aggregate to 4-2.
Obodo, a 19-year-old Nigerian midfielder, evened the score from a 2-1 first-leg loss at Chievo with a perfect header off a corner kick in the 42nd minute.
Diamoutene made it two kicking in a rebound in the 61st. Bothroyd, a British striker who joined Perugia in the off season, sealed victory and qualification for the home team with a diagonal shot six minutes later.
Chievo squandered a couple of first-half scoring chances with Sergio Pellissier and Argentine Mario Alberto Santana.
Perugia-Chievo was the first of eight second-leg matches scheduled between Tuesday and tomorrow.
Today it's Parma versus Venezia, Lazio versus Modena, Palermo versus AS Roma and Reggina versus Inter Milan.
On Thursday defending champion AC Milan, coming off a bitter loss to Boca Juniors in the Intercontinental Cup, takes on Sampdoria at San Siro, Juventus plays Siena and Bologna is at Udinese.
Milan, Roma, Lazio, Juventus and Inter Milan all take first-leg wins into upcoming matches.
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