But the home side were not made to work hard for the points on a blustery night at the Reebok Stadium.
Tottenham came to Lancashire having not lost away from home this season. That record was soon to change, although incredibly Spurs have never won at the Reebok Stadium in previous visits.
Bolton, as they have already shown this season, were up for the challenge and duly extended their winning Premiership run to three games on the bounce, following on from victories over West Brom and Charlton Athletic.
Nolan, after what had been a quiet opening, brought the match into life with a wonder strike after Kevin Davies' neat lay-off.
It was his seventh goal of the season and fourth in the last five games - a splendid achievement considering he spends most of his time in the middle of the park, running forward to support El Hadji Diouf and Davies.
The first half was a scrappy affair with both sides very cautious, maybe showing too much respect for each other having started the season in fine fashion.
And it showed as there was not a clear-cut chance on goal in the opening half-hour, until Nolan, in the 32nd minute, ignited what was turning into a rather dull encounter.
The Bolton midfielder unleashed a fierce 25-yard shot out of nothing - and Tottenham keeper Paul Robinson had no chance.
It should have been 1-1 though, as Jermain Defoe looked to have beaten the offside trap as he fired passed Jussi Jaaskelainen in the Bolton goal. But the linesman ruled the effort out for offside to the annoyance of the Tottenham striker.
Nolan nearly rubbed salt into the wound moments later, but having collected a clever pass from Diouf, the on-song player hit a post with a side-footed shot.
Maybe he should have struck his shot harder, but it would be harsh to criticise him for he was Bolton's best player in the opening exchanges.
Bolton were the better starters in the second half, but the first real chance fell to the visitors. Mido managed to get a shot away in the box, but a body of Bolton defenders got in the way of the ball and the danger was averted.
Defoe also went close in the 73rd minute, but Jaaskelainen was equal to the effort.
Tottenham almost equalised moments later but England defender Ledley King should have done better from close range as Gary Speed cleared off the line.
The visitors also hit the bar in the dying seconds as Jaaskelainen was nearly beaten by a swirling ball in the air.
But Allardyce introduced Frenchman Bruno N'Gotty in the dying stages as Bolton played with three centre-backs to make sure there was no way for Tottenham to grab a point.