Our £1.5m capture from Brighton showed exactly the sort of form that attracted the attention of Glenn Hoddle with goals after 21 and 44 minutes.
Both were poacher's efforts - the first a lethal finish from 12 yards after Gus Poyet's run into the box, the second a dart between goalkeeper and defender to make John Jackson's cross his own before tapping home.
Robbie Keane smashed home his first goal on his first appearance of the season in the second half to complete a good afternoon's work at the Kassam Stadium.
In-between goals, Zamora's play was just as impressive in the first half as he linked up particularly well with Poyet, skipper for the day and a driving force from midfield.
Poyet was everywhere and could have scored a hat-trick of his own in the half - he shot tamely after a one-two with Zamora, his own player blocked a goalbound header and a meaty volley, again from Zamora's assist, whistled inches over.
The second half heralded the arrival of Keane and Steve Carr for Zamora and Hughes for the first time in pre-season.
It was a quieter affair livened when Keane cracked home his goal from 22 yards, a bolt out of the blue that left Cox clutching at thin air.
Keane was inches away from a tap in when Poyet's volley flashed across goal, Cox did well to block Mark Yeates' effort and at the other end, Rob Burch was on his toes to pluck out James Hunt's drive.
8mins: Driving diagonal run into the box by Etherington, shot back across Cox rolled a yard wide.
9mins: Zamora's pace took him away from Bound but Cox equal to powerful shot straight at him.
11mins: Hughes ball over the top diverted just wide by Zamora, tricky chance.
15mins: Low drive from Jackson from half-cleared corner blocked on line by Bound.
21mins: GOAL. Poyet found Zamora in box, yard of space, buried it under Cox. 1-0.
25mins: Surging run from Etherington, delicious one-two between Poyet and Zamora but tame effort at the end from Poyet.
33mins: Quick break from Hackett but Henry back in time to nick the ball away from Alsop.
36mins: Poyet's goalbound header from Anderton's corner hit Jackson and bounced to safety.
38mins: Blondel thunderbolt from 30 yards tipped away well by Cox.
40mins: Zamora teed up spectacular volley from Poyet inches over.
44mins: GOAL. Jackson's cross to near post met by Zamora between Cox and Crosby, tucked into empty net. 2-0.
Half-time: Oxford 0-2 Spurs
Half-time: SUBS. Keane and Carr for Zamora and Hughes.
52mins: Hunt shot well saved by Burch diving to his right.
57mins: Keane picked his spot from Carr's clever cutback but Cox saved low to his right.
63mins: GOAL. Keane blasts one into the roof of the net from 22 yards. 3-0.
69mins: Deep cross from Jackson volleyed across goal by Poyet, Keane inches away from touching home.
79mins: SUB. Yeates for Etherington.
85mins: Yeates and Keane fashioned an opening in the box but Cox out quickly to block Yeates' effort.
Line-ups: Oxford United: Cox, McNiven, Robinson, Crosby, Bound, Hackett (Basham, 62), Whitehead (Musgrove, 88), Hunt (Townsley, 58), Widdrington, Brown (Brooks, 85), Alsop (Blackstock, 75).
Spurs: Burch, Hughes (Carr, 45), Taricco, Jackson (Galbraith, 69), Henry, Perry, Anderton, Poyet, Zamora (Kean3, 45), Blondel, Etherington (Yeates, 79). Subs: Jalal, Foster, Slabber, Barnett.
Bobby Zamora kicked-off his Spurs career in style with a debut double in Sunday's friendly win at Oxford United.