Lambert, below, showed his importance to Saints, first cancelling out a stunning Muhammed Demirci opener and then setting up Emmanuel Mayuka for his first goal in Saints colours.
Youngster Lloyd Isgrove signed off his impressive pre-season with a last minute strike, also his first for the club, to seal the win.
But it was last season’s top scorer Lambert who changed the game after coming on as a second-half substitute for Guly do Prado.
Amid reported interest from West Ham and Reading, Pochettino said: “We count on Rickie.
“We are happy with him. I didn’t know there was any interest in him. This is a surprise for me.”
The St Mary’s boss also allayed fears £12m ace Gaston Ramirez, who again did not take any part in the match, will be leaving.
Pochettino said: “I just listen to Gaston. Not his agent. Gaston is happy here and we expect him to stay and to put a lot into the team.”
The Argentine made eight changes from the side that lost against Schalke on Tuesday, with only Jos Hooiveld, Calum Chambers and Jay Rodriguez keeping their place.
With Nathaniel Clyne picking up a knock in training, rookie Chambers again started at right-back. First choice keeper Artur Boruc was back between the sticks and had to make a flying fingertip save to stop Hugo Almeida breaking the deadlock.
James Ward-Prowse came the closest to a Saints goal after 39 minutes with his low free-kick being tipped around the post as Saints ended the first half the strongest.
But it was Besiktas, the team who finished third in the Super Lig last year and managed by ex-West Ham star Slaven Bilic, who opened the scoring on the 62nd minute through Demirci’s 30-yard wonder strike.
The introduction of Lambert, Luke Shaw and Victor Wanyama at half-time had given Saints new impetus and, after Jason Puncheon had been hacked down on the right wing, the equaliser came.
Jack Cork swung the free-kick into the box, where Lambert was on hand to chest down and rifle past Besiktas stopper Cenk Gonen after 75 minutes.
Three minutes later, Mayuka, who had earlier had a goal chalked off for offside, finally broke his Saints goal drought with a stunning 20 yard left-footed dipping volley after running on to a Lambert through ball.
Sensing a third, sub Steven Davis picked the ball up in his own centre circle with four minutes to go and ran unchallenged through the Besiktas half before seeing his subtle chipped effort come back off the bar.
It was Isgrove who rounded off the confident display with the last kick of the game, curling home left-footed after getting on the end of a Luke Shaw cross.