The Dutchman sealed his move from Chelsea this week and he celebrated in perfect fashion with a goal on 55 minutes.
Zenden raced onto a fine pass from fellow countryman George Boateng before coolly slotting home.
Gaizka Mendieta thrilled the home crowd with a stunning 30-yard drive on 64 minutes and Joseph-Desire Job sealed the win with the third 16 minutes from time.
Mallorca netted a consolation through veteran defender Nadal, but it was not enough to take any gloss off a sparkling Boro performance.
Newcastle slipped to a 2-1 defeat in a prestigious friendly with SPL champions Celtic.
Despite a viral infection sweeping through the Magpies camp, manager Sir Bobby Robson fielded a strong team.
Craig Bellamy was handed a chance to stake a claim for a starting place and he did his cause no harm when scoring on 60 minutes.
However, it was not enough as Mohammed Sylla and new boy Henri Camara sealed a win for The Bhoys.
Welsh speedster Bellamy netted on the hour, collecting a pass from Kieron Dyer before slamming home.
Celtic rallied and were level 12 minutes later when Sylla headed home from a corner.
The comeback was completed two minutes from time when Camara, in his first start since his loan move from Wolves, scored with the aid of a deflection.
Arsenal drew 0-0 with their Belgian feeder club Beveren.
Gunners boss Arsene Wenger took the chance to see Marco Ne and Emmanuel Eboue, who have been on trial at Highbury, in action as they turned out for Beveren against his Gunners.
Christian Schwegler played the first half for Arsenal and the second for Beveren, as Wenger took the opportunity to assess a clutch of players in a game which ended goalless.
Blackburn were beaten 1-0 by Portuguese giants Sporting, a Portsmouth XI were made to work hard for a 3-2 win at Oxford City, while Aston Villa beat Gloucester 3-0.
Villa's new signing Vaclav Drobny played 90 minutes, while Luke Moore was on target in the win.
