Danny Collins, Danny Pugh and Andy Wilkinson are all possible candidates to replace Higginbotham at left-back.
Matthew Etherington was sent off for the visitors for kicking out at Black Cats defender Danny Collins.
Robbie Savage, John Oster and Danny Collins are all absent from the squad.
Azerbaijan should have equalised just after the quarter-hour mark as the quicksilver Zaur Tagizade beat Wales left-back Danny Collins to the byline.
BBC: SPORT | Football | Internationals | Wales 2-0 Azerbaijan
Mensah will now compete for a place in the Black Cats' rearguard with Anton Ferdinand, Danny Collins, Nyron Nosworthy and Paulo Da Silva.
Then Danny Collins, who missed a scoring chance in the first half, saw his header cleared from underneath the bar by Lucas Neill.
Cudicini then palmed Grant Leadbitter's long-range effort away for a corner and from the resulting set-piece Danny Collins outmuscled Terry but his header went wide.
But Danny Collins and Anthony Stokes failed to find the target with flashing first-half headers and Kenwyne Jones could not turn in a left-wing cross.
But Sunderland still had to wait until the 80th minute to get a first effort on target, Danny Collins' header forcing a smart low save from Radek Cerny.
The opening exchanges were pretty feisty and Emmanuel Eboue was stretchered off after a strong challenge from Danny Collins, although the defender was able to return to the field.
Reid hit the top of the bar, Cisse again headed wide of the mark and Danny Collins saw a left-foot shot tipped over by Robert Green as Sunderland searched for an equaliser.
The Caerphilly-born playmaker is the latest off the Cardiff production line of players to move to the Premier League following Chris Gunter, Danny Gabbidon, James Collins and Rob Earnshaw into the top league.
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