They could have taken the lead inside the first minute when Lee Chung-yong picked out Matt Taylor. He was left unmarked in the penalty area but failed to test Heurelho Gomes, sending his effort high and wide.
Gareth Bale, outstanding against Inter, then nutmegged Steinsson but Lee provided back-up and made the clearance.
The Welsh international was seeing plenty of ball and got on the end of a good pass from Luka Modric after 10 minutes. However Bale made a mess of the cross from the left, sending it high over the bar.
Back came Bolton and they made the breakthrough two minutes later, with Tottenham shooting themselves in the foot.
Sandro carelessly lost possession to Fabrice Muamba, who played the ball on to Taylor. He then slipped it through to Davies, whose shot was too strong for Gomes and found the bottom corner.
The visitors hit back and William Gallas tested goalkeeper Jussi Jaaskelainen from distance in the 39th minute after being set up by Modric.
Tottenham were beginning to get into their stride and Younes Kaboul found himself in space following a corner from Bale. But he failed to take advantage of the situation and shot high over the bar.
Redknapp decided to boost his attacking options at half-time and brought on Pavlyuchenko for Wilson Palacios.
Tottenham almost drew level in the 52nd minute following a superb free-kick from Bale which shaved the outside of Jaaskelainen’s post.
Bolton hit back immediately and Johan Elmander saw his effort booted clear by Gomes with Paul Robinson and Taylor also playing their part in a flowing move.
Tottenham again found themselves on the back foot when Gary Cahill strode forward but he sent his effort wide of the target.
Bolton extended their lead in the 56th minute thanks to Steinsson’s first goal of the season. The Icelandic full-back, charged with the task of shadowing Bale, broke clear to get on the end of a cutback from Elmander to fire a shot beyond Gomes and give his side some breathing space.
Tottenham were stung but Hutton sent a fine ball into the area only to see Sandro fail to get a decent touch.
Bolton were looking to build on their lead and Elmander came close in the 68th minute, finding the side-netting.
However, the hosts made it 3-0 after 75 minutes with Davies’ second goal of the game, which came from the penalty spot.
Benoit Assou-Ekotto was punished for tripping Lee and Davies calmly slotted the ball home.
The goal came after a spell of pressure from Bolton with Taylor seeing his shot come back off the post and Muamba firing wide from close range.
Tottenham were left reeling but pulled a goal back in the 79th minute thanks to a magnificent solo effort from Alan Hutton.
They were given real hope when Pavlyuchenko grabbed a second with a superb volley nine minutes later – only for substitute Petrov to wrap things up.