Fredi Kanoute and Robbie Keane both opened their accounts for the season to put us in the driving seat at Boundary Park.
Those goals - Kanoute's powerful header, Keane's cool finish - were the difference between the sides in what was a relatively tight encounter for 65 minutes.
Jermain Defoe entered the fray for Keane after the Irish striker made it 2-0 and it took just five minutes for him to make his mark with a smart finish to make the tie safe at 3-0.
The game then looked to be petering out before an amazing finale.
Goran Bunjevcevic bagged his first goal for the club since joining at the start of the 2001-02 season when he capitalised on Oldham keeper Craig Mawson's error from Pedro Mendes' corner after 87 minutes.
Anthony Gardner followed up two minutes later with only his second goal for the club - a sweet 25-yard drive into the bottom corner to make it 5-0.
And with cries of 'we want six' from a healthy Spurs following, the half-dozen was delivered by Kanoute, rifling the ball into the roof of the net after being played in by Rohan Ricketts.
It was a little harsh on an Oldham side who were always in the tie until Keane's strike just after the hour.
They had threatened Kasey Keller's goal without really carving out a clear-cut chance - a couple of wayward shots the sum total of a robust first half display.
With seven changes from Sunday's draw at Chelsea including the return of Keller in goal and first starts of the season for OJ Mabizela, Goran Bunjevcevic and Anthony Gardner, it was no surprise we took a little while to get going.
Kanoute eventually opened the scoring after 37 minutes with a classic header from Keane's corner before roles were reversed and Keane volleyed Kanoute's knock down over from six yards just before the break.
It wasn't too long before Keane notched his first of the season though as he capitalised on a defensive mix-up before slotting home from a tight angle.
If that goal knocked the stuffing out of the home side, his replacement Defoe ended it as a contest five minutes later, sliding home one-on-one.
That looked just about that until the mad last five minutes turned 3-0 into 6-0.
The victory extended our unbeaten start to the season to seven matches with three wins, four draws, five clean sheets and just two goals conceded.
MINUTE BY MINUTE
1min: Moment of concern as Keller darted out of box to meet Johnson, slight indecision with Gardner but eventually able to clear.
5mins: Deep free-kick from Eyres, Arber climbing at far post but header never a danger.
7mins: Keane attempted dink from edge of box easily collected by Mawson.
15mins: Kanoute burst down left, cross looking for Keane, angle too tight to do anything but volley back across six-yard line.
16mins: Appleby onto ball as Redknapp stumbled, 30-yarder flew wide.
19mins: Decent move across pitch, Redknapp eventually played in Davies, cross to far post missed by Brown but fell to Jackson at far post who drove across box, ball managed to evade everyone.
20mins: Keller out quickly to clear as Johnson went for ball over the top.
29mins: Corner played to edge of box to Eyres, cut inside Brown but shot high and wide.
37mins: GOAL. Kanoute powered home Keane's corner from eight yards. 1-0.
45mins: MISS. Redknapp floated ball into Kanoute, he headed down to Keane who lifted ball over the bar from six yards.
Half-time: Oldham 0, Spurs 1
48mins: CLOSE. Best move of match involving Davies, Keane and Jackson ended with Brown curling just wide from edge of box.
51mins: CLOSE. Killen pounced on loose ball and snapped volley just wide.
53mins: Johnson tricks on edge of the box but low shot always going wide.
60mins: Kanoute spun away from two defenders and fired just over from 20 yards.
61mins: SUB. Mendes for Redknapp.
63mins: SUB. Jack for Killen.
65mins: GOAL. Jackson pass, Keane took advantage of mix up between Mawson and Arber and slotted home from tight angle. 2-0.
67mins: SUB. Defoe for Keane.
70mins: CHANCE/SAVE/OFF LINE. Keller saved point-blank from Arber, ball fell twice to Holden eight yards out but Gardner and King blocked both attempts.
70mins: GOAL. Quick break from that Oldham attack, Brown and Jackson involved, Defoe suddenly one on one and finished in style.
71mins: SUB. Ricketts for Davies.
85mins: Defoe so lively in the box after good work from Bunjevcevic, turned away from Haining before striking into side-netting.
87mins: SUB. Barlow for Eyre.
87mins: GOAL. Mawson spilled Mendes corner and Bunjevcevic volleyed in his first goal for the club. 4-0.
89mins: GOAL. Gardner picked ball up in space before drilling low shot into corner from 25 yards. 5-0.
Injury time: SAVE. Eyres effort heading for top corner but Keller tipped over at full stretch.
Injury time: GOAL. Knocking ball around now, Mendes involved heavily, Ricketts into Kanoute who smashed into roof of net. 6-0.
Line-ups: Oldham: Mawson, Holden, Griffin, Haining, Arber, Boshell, Appleby, Eyre (, Eyres, Killen (Jack, 63), Johnson. Subs: Treacy, Lomax, Hall.
Spurs: Keller, Mabizela, King, Gardner, Bunjevcevic, Davies (Ricketts, 71), Redknapp (Mendes, 61), Brown, Jackson, Kanoute, Keane (Defoe, 67). Subs: Robinson, Pamarot.
Referee: R Beeby.
Our Special K's got back on the scoresheet before a late flurry of goals saw us home with a flourish in the Carling Cup at Oldham on Wednesday night.