Igor Jesus opened the scoring shortly before half-time, netting his second goal in as many pre-season games.
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Arnaud Kalimuendo doubled Forest’s advantage just three minutes after the restart, before Taiwo Awoniyi completed the scoring moments later following a fine team move.
The victory marked the club’s second successive pre-season win after Saturday’s 2-0 triumph over Notts County.
Oliver Glasner’s side still have two games remaining during their Algarve training camp, including a behind-closed-doors clash with Vitória S.C. before facing Portuguese giants Sporting CP on Friday, July 31.