Karadas' goal five minutes from time cancelled out Bolton midfielder Khalilou Fadiga's first-half opener on 69 minutes.
The Senegalese international had earlier ballooned a penalty high and wide into the Fratton End on the stroke of half-time.
Redknapp gave debuts to new boys Wayne Routledge and Andres D'Alessandro and the Argentinian international's class was given its first airing on 12 minutes as he ghosted inside Fadiga and Kevin Nolan at the heart of the Bolton midfield.
It was the away side though who fashioned the first real chance as the game as Fadiga's sweeping free-kick fell at the feet of Stelios. The in-form Greek star scuffed his first effort but managed to have a second bite and saw his stretching volley drift wide.
Pompey took some time to get going and on 31 minutes a sweeping move involving Sean Davis and Benjani Mwaruwari saw D'Alessandro fire a right-foot effort narrowly over.
Bolton's penalty on the stroke of half-time was somewhat controversial as Matt Jansen played Stelios behind the flat-footed Pompey back four and although the midfielder rounded Dean Kiely, his fall was theatrical.
Referee Dermot Gallagher though pointed to the spot and it was poetic justice when Fadiga's penalty soared well wide of Kiely's goal.
D'Alessandro was at the heart of everything for the home side and he created an effort for substitute Svetoslav Todorov just after the break.
The Bulgarian did everything right cutting inside Tal Ben-Haim, but he was off-balance as his right-footed shot was sliced wide.
Pompey, against the run of play, nearly went behind on 68 minutes when a mix-up between former Tottenham team-mates Pedro Mendes and Davis left Pompey seriously outnumbered at the back.
Jansen rounded Kiely and, from a tight angle, tried to pick out Davis but Andy O'Brien had got back just in time to head the ball clear.
Bolton's fluke lead came when Matt Taylor bundled over Stelios and Fadiga stepped up to swing in a left-footed free-kick which evaded both Taylor and then Kiely before drifting harmlessly into the far corner of the goal.
As D'Alessandro and Routledge tired so did Pompey's attacking options, but they somehow managed to claw an equaliser.
First Todorov had a effort cleared off the line by Joey O'Brien and then a minute later Routledge's cross was directed in to the goal by a smart right-footed volley from on-loan Benfica striker Karadas.