Christian Benteke celebrates scoring Crystal Palace's second goal against Bournemouth
The fact victory was achieved on the back of a clean sheet – Palace’s first in the league for two months – only added to Allardyce’s satisfaction.
Goals by Scott Dann and Christian Benteke might have gone some way to make the manager reconsider his angry opposition to scheduling fixtures on deadline day.
But while Palace chairman Steve Parish sat in the directors’ box ,his phone glued to his ear, trying to tie up last-minute deals, Allardyce was put through the mill on the touchline.
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After Dann put the visitors ahead immediately after the break, Allardyce’s side held on before Benteke’s second in added time fired hope they can escape the bottom three.
Allardyce admitted Palace were desperately short of confidence but insisted he had seen enough in the last two games – home defeats by Everton and Manchester City – to convince him they could turn things around.
The return of Wilfried Zaha after his appearance at the African Nations Cup with Ivory Coast gave Palace a lift, as did the inclusion of Patrick van Aanholt following the left-back’s £14 million arrival from Sunderland.
And Zaha quickly offered a glimpse of what Palace had been missing in recent weeks when he created a chance out of nothing, turning twice 20 yards out before sending a low shot against a post.
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Eddie Howe’s Cherries have been struggling and they were again exposed at a Palace free-kick after Jack Wilshere fouled Zaha, only for Benteke to fire well wide. There were worrying signs for Allardyce, too, when first Josh King and then Junior Stanislas saw goalbound efforts deflected narrowly wide.
But Zaha remained the player most likely to break through and he should have done better when he turned Brad Smith only to send a close-range shot straight at Artur Boruc.
For once, though, the Ivorian was not involved when Palace did take the lead less than a minute after the restart.
Instead it was the aerial strength of centre-backs Dann and Damien Delaney who combined with Delaney flicking on Jason Puncheon’s cross to Dann who finished first time.
Palace had to hang on, though, as the Cherries rallied but Benteke sealed it by heading home substitute Andros Townsend’s cross.
Bournemouth (4-2-3-1): Boruc 7; A Smith 6, S Francis 7, S Cook 7, B Smith 5 (Arter 68 6); Surman 6, Wilshere 7; Stanislas 7 (Ibe 61 6), King 7, Fraser 6; Afobe 6 (C Wilson 61 6). NEXT UP: Everton (a), Sat PL.
Crystal Palace (5-4-1): Hennessey 6; Ward 6, Tomkins 6, Dann 7, Delaney 7, Van Aanholt 7; Zaha 9, Cabaye 6 (Ledley 76), McArthur 7 (Townsend 75), Puncheon 7; Benteke 6. Booked: Ward. Goals: Dann 46, Benteke 90. NEXT UP: Sunderland (h), Sat PL.
Referee: J Moss (West Yorkshire).