Keane opened the scoring from the penalty spot in the first half before Jermain Defoe stamped his class on procedings with another classy finish six minutes from time.
The home side grabbed a consolation goal in the 88th minute to send most of the packed 7,044 crowd home happy.
Mendes, our summer recruit from FC Porto, sprayed the ball about in the first-half of what was, in honesty, a match lacking any real goalmouth action.
Keane opened the scoring after 18 minutes. Johnnie Jackson did the damage down the left, a burst into the box that led to handball from Matt Hocking and Keane dispatched the penalty clinically to Andy Woodman's right.
Keane was involved in the only other notable incident of the first half, a majestic volley from 20 yards that dipped just over.
The action picked up a little after the break and Kasey Keller was forced into a spectacular tip over from Richie Hanlon's curler after 54 minutes.
Defoe, who has looked sharp so far in pre-season, lashed his first sight of goal just wide from 25 yards four minutes later.
The England striker then shot straight at Woodman but it wasn't long before he made his mark, picking up Rohan Ricketts' pass, flashing past the defender and rolling home a cross Woodman.
Borough responded with a decent finish from Brian Quailey, who dinked the ball over the advancing Keller two minutes from time.
16mins: First serious threat at either end, Elding turned O'Donoghue before driving across face of goal. Ball eventually fell to McAllister, who shot tamely at Keller from 20 yards.
18mins: PENALTY/GOAL. Jackson burst down the left, cross handled by Warner, penalty slotted home by Keane. 1-0.
23mins: Long ball from Warner would have found Elding through on goal but striker failed to control.
30mins: Speculative volley by Mendes from 30 yards flew wide.
32mins: Flighted, curling free-kick from Bulman caught under crossbar by Keller.
34mins: Great block from Hocking to deny Keane from close range.
40mins: Malcolm teed up spectacular volley by Keane that dipped just over from 25 yards.
Half-time: Stevenage Borough 0, Spurs 1
52mins: Ricketts half-chance in box blocked by Hocking.
54mins: SAVE. Keller at full stretch to tip Hanlon's 25-yard curler onto the bar and over.
57mins: CLOSE. Defoe's first sight at goal, a 20-yard scorcher just wide.
63mins: Ricketts worked some space but Rogers dived in to block shot.
73mins: Surging run from Ifil, carried ball 40 yards, attempted shot blocked by Gould.
77mins: Defoe lost two defenders in a turn in the box but fired straight at Woodman.
84mins: GOAL. Ricketts injected pace into move, fed Defoe who strolled away from defender and slotted into corner. 2-0.
88mins: GOAL. Hanlon pass into Nurse, he flicked it around the corner for Quailey to dink over Keller. 1-2.
Line-ups: Stevenage Borough: Stevenage Borough: Woodman, Warner, Gregory (Gould, 62), Quinn (Nurse, 67), Rogers, Hocking (Goodliffe, 65), Brady (Boyd, 45), Gruff (Quailey, 45), McAllister (Hanlon, 45), Elding (Maamria, 45), Bulman (Hodgson, 71).
Spurs: 1st half: Keller, Kelly, Taricco, Mendes, O'Donoghue, Bunjevcevic, Yeates, Marney, Malcolm, Keane, Jackson.
2nd half: Keller, Ifil, Mabizela, Doherty, McKie, Defoe, McKenna, Ricketts, Hughes, O'Hara, Malcolm.
A night of firsts at Broadhall Way - Jacques Santini's first friendly win, Robbie Keane's first goal in pre-season and a first start for Pedro Mendes.