Bolton keeper Jussi Jaaskelainen was indeed man-of-the match, making superb saves from Sean Davis (twice), Matthew Taylor and Nwankwo Kanu in repelling a Portsmouth side who endeavoured for 90 minutes to break through a stubborn and spirited Bolton defence.
Bolton's goal came after 22 minutes, Linvoy Primus' defensive header falling to Nolan on the edge of the box who sent a sweet volley into the bottom right hand corner of David James' goal.
Portsmouth dominated possession but were restricted to opportunistic shots by a well-drilled and brave Bolton defence, Tal Ben Haim playing at full back with all three left backs out and the likes of Nolan, Gary Speed and Abdoulaye Faye hurling themselves in front of everything.
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The best opportunity came to the impressive Davis when he flicked the ball onto the post after a Benjani knockdown, replays showing Jaaskelainen to have touched the ball onto the woodwork.
The former Fulham man was denied by the Finn later in the second half after ghosting past four Bolton challenges, his long-range shot palmed away for a corner.
The second half saw a true backs against the wall performance from Bolton, who barely passed the Portsmouth halfway line as they absorbed wave after wave of Pompey pressure.
The late introductions of Manuel Fernandes, Lomana Tresor Lua Lua and David Thompson could not change things, the former and latter going close along with Sol Campbell and Glen Johnson.
It was destined to be Bolton's night, who move to sixth while Pompey drop a place to third after their first defeat and goal against of the season.
Allardyce hailed his side's fight and spirit in the match.
"I think it was a typical backs to the wall performance from 11 very committed players," Big Sam told Sky Sports afterwards.
He added: "We've been missing that level of defending away from home this season.
"There was some absolutely desperate defending tonight, people willing to put their bodies in where it hurts and of course a wonderful goal to give us the win."
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