Paul Merson, chosen for the England B squad for the friendly international with Chile at West Bromwich next week, scored twice to take his goal tally for the season to 14.
Middlesbrough, who gave a loan debut to the Liverpool midfielder Michael Thomas, went ahead after 31 minutes through Craig Hignett, who cut in from the left, passed to Nigel Pearson and then followed up with a shot into the roof of the net after his captain's effort had been blocked.
Shortly afterwards, Robbie Mustoe shot over for Middlesbrough from four yards. But the hosts stepped up the pace again, and after 38 minutes Merson moved on to a Vladimir Kinder pass to score a fine goal.
Merson chipped over the bar after 55 minutes when Mikkel Beck presented him with a good scoring chance and a few minutes later the former Gunner was again off target. But Merson was not to be denied and added a third after 65 minutes though, according to the visitors, he should have been ruled offside.
Middlesbrough: Schwarzer; Stockdale, Kinder, Vickers, Pearson (Liddle, 81), Mustoe (Summerbell, 81), Hignett, Townsend, Beck, Merson, Thomas. Substitute not used: Moreno.
Tranmere Rovers: Simonsen; Frail (Morgan, 83), Thompson, McGreal, Challinor, Irons, Jones (Morrissey, 70), Parkinson (Branch, 53), Kelly, O'Brien, Mellon.
Referee: J Kirkby (Sheffield).