Last season's Academy boys Ronnie Henry and Lee Barnard also enjoyed their opening first team outings.
The first half team saw us into a 3-0 lead at the break with goals from Johnnie Jackson and two from Darren Anderton before Glenn almost completely changed the team at half-time with only Henry surviving the cut.
Every time Carr touched the ball in the opening stages there was a ripple of anticipatation around the ground, but it was new boy Acimovic stealing the show.
The Slovenian produced an extravagant piece of skill on the left of the Stevenage penalty area and left his marker in a heap before just failing to find Poyet with a cross after only a couple of minutes play.
He then proceeded to delight the packed crowd at Broadhall Way with flashes of brilliance. Early evidence suggests that thrills could be on the menu where Acimovic is concerned.
On 11 minutes he created space on the right to cross onto the head of Poyet, whose effort lacked power but still managed to cause confusion in the Stevenage rearguard.
Sullivan's only scare in the opening 20 minutes was nearly getting caught out by a powerful Stirling throw from the left.
Spurs set out with three central defenders, Ronnie Henry playing on the right of Bunjevcevic and Richards. Johnnie Jackson occupied the left wing-back role with Carr on the right.
New boy Rohan Ricketts and Anderton operated in the centre with Poyet and Acimovic playing behind Doherty up front.
On 23 minutes Acimovic nearly opened the scoring when he pounced on a loose ball from about 15 yards out. Home keeper Mark Westhead did well to block at full stretch.
The deadlock was broken on the half an hour mark, a sweeping pass from Acimovic put Jackson in the clear down the left, he advanced towards the penalty area and lofted a superb chip over keeper Westhead and into the empty net.
Poyet nearly doubled the advantage just minutes later with another lob, but this one just cleared the post with Westhead beaten.
On 36 minutes the lead was doubled, a weak mis-directed pass into the Stevenage area appeared a simple task for Jamie Campbell and keeper Westhead to deal with. But they both left it to each other and Anderton was on hand to seize on the loose ball and, despite Westhead attempting to haul him down, slide the ball into an empty net.
A minute before the break Spurs extended the lead when the ball fell to Anderton on the edge of the area slightly towards the left. Darren hit the ball first time low on the volley and, with the aid of a slight deflection, the ball drifted past Westhead and into bottom left hand corner of the net.
There was almost a complete team change at half-time, with only Henry remaining from the starting X1.
Stevenage actually had the first shooting chance of the second period, but Hirschfeld dealt comfortably with the threat.
There was a flurry of action nine minutes into the half when Etherington began to torment his marker down the left and his whipped inswinging cross evaded the keeper and had to be headed out from under the bar. Seconds later, Barnard chested a cross ball into the direction of Redknapp who fired his effort just over.
Spurs were totally bossing the play without finding the killer final pass until 68 minutes when a Barnard ball from the right was picked up in the area by Leonhardsen. Leo advanced and looked set to shoot before slipping the ball in the direction of Rebrov who clipped the ball home.
1st half team: Sullivan, Carr, Jackson, Henry, Bunjevcevic, Richards, Anderton, Poyet, Doherty, Acimovic, Ricketts.
2nd half team: Hirschfeld, Thatcher, Perry, Henry, Leonhardsen, Redknapp, Etherington, Bortolozzo, Davies, Rebrov, Barnard.
By Richard Hubbard at Broadhall Way
Spurs began their pre-season programme with a convincing 4-0 over Stevenage in a match that marked the return of Stephen Carr from injury and the first games of Milenko Acimovic and Rohan Ricketts.