Portsmouth showed there was life without Harry as they achieved their first away win of the season.
Pompey, with Velimir Zajec in charge following Redknapp's resignation, went ahead on the stroke of half-time when captain Arjan De Zeeuw headed in a Gary O'Neil free-kick.
It was Bolton Wanderers' second successive home defeat, piling on more disappointment, especially as they were up against a team torn apart by a spate of injuries and the midweek turmoil off the field.
Yet the home side were never able to mount enough pressure in front of goal to test a Portsmouth defence that grew stronger as the match went on.
Apart from a couple of El-Hadji Diouf attempts at goal, Portsmouth keeper Jamie Ashdown producing a brilliant one-handed save to deny him in the first half.
The Wanderers attack failed to score for the first time at home this season, while it was Pompey's first ever win at the Reebok.
Wanderers had the luxury of being able to choose from a full strength squad and Sam Allardyce made two changes from the side that took a point off Chelsea at Stamford Bridge in their previous game.
Greek international Stelios Giannakopoulos displaced top scorer Henrik Pedersen who was dropped to the bench, along with midfield man Kevin Nolan, who made way for Ivan Campo.
In contrast Zajec's first line-up was more about who was out rather than who was in.
A spate of injuries seriously limited his choice, particularly up front, where injuries to Yakubu, Diomansy Kamara and Lomana LuaLua left Ricardo Fuller as the only recognised striker.
Ashdown continued in goal in place of the injured Shaka Hislop, but there were some good news with the return of Steve Stone after being out since September with ankle trouble.
Neither side were able to show much attacking flair in the opening quarter as play reached something of a midfield stalemate.
However, in the 25th minute Diouf tricked his way into the area, and when he passed inside to Stelios it took some determined defending to keep him out.
Three minutes late Portsmouth were grateful to keeper Ashdown, who stuck out a right hand to knock away a Diouf shot that looked destined for the back of the net.
Portsmouth's early attacks were limited to a long-range snap shot by Matt Taylor, the Pompey attack being held at bay by the solid combination of Bruno N'Gotty and Radhi Jaidi.
But when Jaidi was caught out in the 38th minute it offered Patrik Berger the chance to shoot Portsmouth in front, but although on target, it lacked pace to beat Jussi Jaaskelainen, who saved fairly comfortably.
Diouf had been the focal point of many of Wanderers' attacks and when Kevin Davies crossed to the far post, the Senegalese international's diving header was deflected away for a corner.
Yet on the stroke of half-time Portsmouth grabbed something of a shock lead.
O'Neil took a disputed free-kick after Nicky Hunt had been harshly penalised for a foul and in a packed six-yard box, De Zeeuw managed to head the ball past Jaaskelainen.
Diouf and Davies in quick succession almost put Wanderers level within a minute of the re-start before Jaidi was guilty of a bad miss when he put the ball over from the six-yard line.
Gary Speed, still looking for his first goal for Wanderers, planted a header straight into Ashdown's hands, but Portsmouth still posed a threat. Particularly when Berger ended a run from the halfway line with a shot that whisked past a post.
Ricardo Gardner was injured in trying to halt the move and was stretchered off to be replaced by Fernando Hierro.
The Wanderers defence was starting to look anxious and there was another alarm in the 61st minute when Jaaskelainen was forced into a save at the near post from Fuller's first-time shot.
Diouf's claim for a penalty when he was brought down by Andy Griffin were turned down by referee Dunn, then Linvoy Primus had to concede a corner as another of their attacks was stalled by the Pompey defensive wall.
Jay-Jay Okocha was a whisker wide with a free-kick from the edge of the area, but generally the Portsmouth defence was doing a more than capable job of frustrating the home side, while causing some alarm with breakaway moves.
It was a ploy Wanderers had used themselves in many away games, but it was one they found hard to handle when confronted with it at home.
Man of the Match: Steve Stone Â– The one-time England international returned from a long injury lay-off to bolster a midfield that denied Wanderers much-needed breathing space.