The four summer signings played 45 minutes each as goals from Fredi Kanoute, Mido and Jermain Defoe accounted for the Conference outfit.
Lennon and Routledge provided assists for two of those goals as Martin Jol employed two teams for our first friendly.
Winger Lennon caught the eye in the first half. The youngster was involved in most of our attacking play, showed his pace in one lightning break and set-up the opening goal for Kanoute a minute before the interval.
Indeed, Lennon could have opened his account on a couple of occasions only to drag a shot wide after 23 minutes and then fire over from Keane's clever cut back after 34 minutes.
He turned provider though as we went ahead a minute before the break. Keane started the move by pushing the ball to Lennon on the right, he cut into the box and laid it into the path of Kanoute who finished well across keeper Julian from 10 yards.
Other chances included Keane's 20-yarder well tipped aside by Julian and Tainio's header unfortunately straight at Julian from 10 yards.
Routledge was one of 11 changes at half-time as Martin Jol opted to field a completely new side for the second half.
Stevenage had their best spell in the opening 15 minutes of the half but missed two golden chances as first Williams headed wide of the mark and then Nurse somehow volleyed over from six yards.
That was the key for us to take control again and it was soon 2-0 as Mido latched onto a loose ball from Andy Reid's corner and lashed into the top corner from 15 yards.
Stevenage's second half keeper Gore saved superbly to keep out Defoe twice from point-blank range but the England striker wasn't going to be denied his goal and finished in style from Mido's pass with seven minutes left.
GUIDE TO THE ACTION
9mins: Good interplay between Kanoute and Keane, Keane released Lennon down the right, reached byline, not enough power on cross to reach Kanoute in box.
17mins: Well-worked free-kick routine as Carrick rolled ball into Keane who laid back for Marney to strike, blocked bravely by Bulman.
21mins: Free-kick half-cleared, Henry onto loose ball but hit volley into ground, easily gathered by Cerny.
21mins: Keane attempted volley from 18 yards but didn't get enough on it.
22mins: SAVE. Keane in space 20 yards out, decent shot saved well low to his right by Julian.
23mins: CHANCE. Kanoute break, fed supporting Lennon, cut inside Henry but scuffed shot wide from 16 yards.
31mins: Deflection took all pace off Kanoute's 20-yarder.
34mins: CHANCE. Keane beat offside trap down right, skipped past Gregory, clever cut back picked out Lennon who fired over from 16 yards.
39mins: Lightning break from Lennon left defenders in his wake, played ball into Kanoute, 12 yards out, crowded out before he could get shot off.
43mins: Kanoute measured cross met on the full by Tainio but header straight at Julian.
44mins: GOAL. Keane liad ball into Lennon, he squared to Kanoute who finished well, side footing beyond Julian into far corner from 10 yards.
Stevenage 0, Spurs 1
Half-time: Stevenage 0, Spurs 1
Half-time: SUBS. Full second half team brought on by Martin Jol (line-up below).
50mins: CHANCE. Williams cross headed wide by Stamp unchallenged from 12 yards.
60mins: Routledge darted into box, fed Mido, cut back was on for Defoe but delayed slightly and Defoe's shot eventually blocked.
62mins: MISS. Sullivan robbed Reid in left-back position, cut into the box, crossed for Nurse who somehow lifted shot over from six yards.
65mins: Defoe released Mido, tight angle, Henry blocked shot.
66mins: SAVE. Fine move as Routledge laid in supporting Kelly, cut back to Defoe, six yards out, Gore somehow managed to deflect wide.
67mins: GOAL. From corner, ball not cleared, Mido latched onto it and lashed into top corner from 15 yards.
Stevenage 0, Spurs 2
72mins: SAVE. Gore brave block to deny Defoe at point blank range after Dawson flicked on Reid's corner.
73mins: Two superb blocks denied El Hamdaoui from close range.
74mins: Mido chipped pass to Reid, 25 yards out, control and half-volley a couple of yards wide.
78mins: Reid's free-kick not enough power to trouble Gore.
80mins: Decent Stevenage move ended with Stewart chance, 10 yards out, Fulop took pace off shot and Bunjevcevic completed clearance.
83mins: GOAL. Routledge burst and laid perfect pass to Defoe who took ball around Gore before slotting into empty net.
Stevenage 0, Spurs 3
86mins: Lovely flicked pass from Reid released Mido who shot over on the stretch.
89mins: SAVE. Webster 30-yarder produced fine one-handed save from Fulop.
Stevenage Borough: Julian, Warner, Gregory, Williams, Maamria, Elding, Boyd, Hocking, Bulman, Burquez, Henry. Subs: Gore, Quinn, Nurse, Weatherstone, Stamp.
Spurs: 1st half: Cerny, Marney, Jackson, Carrick, Davenport, Huddlestone, Lennon, Tainio, Kanoute, Keane, Yeates.
2nd half: Fulop, Kelly, Edman, Dawson, Bunjevcevic, Routledge, Mendes, El Hamdaoui, Reid, Mido, Defoe.
Aaron Lennon, Wayne Routledge, Teemu Tainio and Tom Huddlestone made their debuts as we made a positive start to pre-season at Stevenage on Saturday.