Despite the talismanic David Silva, who had scored four goals in his past three outings, missing a league game for the first time this season, Pep Guardiola's all-conquering juggernaut rolled on to move 14 points clear of nearest rivals Manchester United at the top of the table.
Ilkay Gundogan's free header from a corner gave City an early lead before Kevin De Bruyne doubled their advantage with a left-footed drive 20 minutes from time.
The home side could even afford to see substitute Gabriel Jesus miss a penalty before Sterling bagged a late brace, taking the England international's tally for the season to 15.
Christian Eriksen struck a late consolation but Tottenham, who will drop to seventh if Liverpool avoid defeat at Bournemouth on Sunday afternoon (Monday morning AEDT), were thoroughly outclassed on the road, meaning they have now claimed just one point from their last five away trips away from Wembley Stadium.
The result sees Guardiola equal the best winning streak he oversaw while in charge of Barcelona, though his current crop are still three shy of matching the 19-game run his Bayern Munich squad managed in the 2013-2014 Bundesliga campaign. On this form, it is hard to see when the run will come to an end.
Gundogan was the man chosen to fill Silva's void and he took full advantage with a 14th-minute opener.
Tottenham failed to pay any attention to the stand-in at Leroy Sane's out-swinging corner from the left, allowing the Germany international to drift in unmarked to stoop down and nod his team in front.
That the gap remained at one through to half-time was largely down to two men - Hugo Lloris and Craig Pawson.
Tottenham's busy goalkeeper denied Sergio Aguero, Gundogan and Sane before the break, while the visitors were grateful when Pawson, the referee who awarded Everton a controversial penalty for a push by Liverpool's Dejan Lovren during last weekend's Merseyside derby, failed to spot Danny Rose's blatant two-handed shove on Eliaquim Mangala.
Despite leaving both Harry Kane and Son Heung-min up front, the visitors failed to register a shot on target in an opening half that saw patchy fog descend over the ground.
Their attacking vision appeared to be a little clearer despite the conditions after the break, with Kane finally forcing Ederson into a save with a long-range drive that required pushing around the goalkeeper's right post.
City, though, demonstrated why their defence deserves as much praise as their high-powered attack this season. They weathered the storm and, as Tottenham were forced to throw bodies forward, capitalised on the counter-attack.
Not long after receiving a heavy challenge from Dele Alli that only resulted in a yellow card, De Bruyne grabbed the all-important second goal when lashing the ball beyond Lloris with his left foot.
De Bruyne was fouled by compatriot Jan Vertonghen to earn City a penalty soon after, only for Gabriel Jesus to send the spot-kick against the woodwork.
Sterling failed to convert the rebound too, but could not miss the two late chances that came his way.
The England winger first tapped in from a free-flowing move involved Gundogan and Sane, before finishing another devastating City attack from close range.
Eriksen had the last word, denying Ederson a clean sheet when his low drive fizzed into the net, but Tottenham barely celebrated the strike, well aware they had been outplayed by the league's runaway leaders.
