Harry Kane put Spurs ahead with a controversial penalty early in the second half, the England international claiming his 15th goal in his last 17 league games.
City, yet to beat a top-six side this season, equalised through teenage substitute Kelechi Iheanacho.
But City were consigned to consecutive home defeats for the first time since December 2008 when Eriksen beat Joe Hart in the 83rd minute to celebrate his milestone with his sixth goal of the season.
City, beaten for the first time in the league this season with fit-again captain Vincent Kompany in the side, are now six points behind league leaders Leicester City, while Tottenham's fifth successive league win has raised their hopes of a first league title since 1961.
Arsenal's last-gasp 2-1 win over Leicester earlier in the day had opened the way for both of these sides to reinforce their title credentials.
But it also meant a share of the points would not be a disaster and the result was a cagey opening in which neither side was prepared to gamble too soon.
Tottenham's record at the Etihad Stadium, where they had lost on their previous five visits, may also have made them wary of over-committing, although there was no shortage of confidence in the way in which Mauricio Pochettino's side looked to keep possession.
Tottenham have the best defensive record in the league and were rarely troubled at the back in the first half, with City's best moments coming either from counter-attacks or when the visitors over-played.
The combination of David Silva and Raheem Sterling looked City's best bet to open up Tottenham's back line, with Sergio Aguero, scorer of 10 goals in eight Premier League appearances against Tottenham, also constantly looking to exploit any gap.
But City's only two real sights of goal before the break came via set-pieces, with Aguero volleying over and Sterling seeing a shot blocked by Danny Rose.
Left-back Rose was heavily involved in a lot of Spurs' best moments, but for all the Londoners' composure they managed only one shot on target in the first 45 minutes, a swerving strike from Eriksen that Hart beat away.
And it was Rose who was instrumental in Tottenham taking the lead eight minutes into the second half.
City had just missed the best chance of the game, Aguero slicing an effort wide from the corner of the six-yard box after a deflected Yaya Toure cross had looped into his path, when the visitors were awarded a penalty after Rose's cross hit the jumping Sterling.
It was a big call from referee Mark Clattenburg, as replays suggested the ball had struck Sterling's side, but Kane kept his composure to score from the spot and claim his 19th goal of the season.
City's response was instant as Toure curled a free-kick against the crossbar from 25 yards out.
They were unable to build on that and frustration was beginning to show on the pitch and amongst the home supporters when Iheanacho struck to make it 1-1 with 16 minutes left.
The 19-year-old had only been on the pitch for eight minutes when he met a low cross from Gael Clichy with a thumping left-foot finish from 10 yards out to claim his ninth goal of a breakthrough season.
City pressed for the winner, but instead it was Tottenham who gained a potentially crucial victory.
Substitute Erik Lamela released Eriksen to slide the ball past Hart with seven minutes to go and edge his side closer to an increasingly feasible title triumph.
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