Much had been made of Sterling's profligacy before the game, although the winger finally netted to put City in the driving seat after 72 minutes, the England worldwide smashing home from close range after Lloris had originally saved a shot from Jesus.
Man City came into the tie a wounded team, after suffering a derby heartache against Manchester United last weekend and mid-week's frustrating Champions League exit in the quarter finals. Gundogan does lack the defensive aptitude that Fernandinho has and Pep accounted for this by pulling Fabian Delph into the midfield from his left back position for much of the game.
After a quiet start to the second half, City could have extended their lead in the 64th minute when Jesus broke through on goal, but the forward fired well wide with only Lloris to beat.
"What they lived in the last week was so unfair but they deserve (to win the league) and now we have a match ball".
However, the Gunners now risk the ignominy of finishing the season seventh behind Burnley after a fifth consecutive away league defeat as they lost 2-1 at Newcastle yesterday.More news: Guardiola will play golf as City await title
On return for the second half, Spurs came with a zeal to overturn the result in their favour, as they mounted pressure on their visitors, but all their efforts were unproductive in the early minutes of the second stanza.
Kane at least returned the favour as Eriksen scored in the 42nd minute.
The challenge looked to have been outside of the box, but referee Jon Moss pointed to the spot for a City penalty.
After the miss, both teams quickly introduced new players to their sides - as Erik Lamela made way for Heung-Min Son in a tactical substitution, while Nicolas Otamendi replaced Leroy Sane to beef up the defence line. England winger Sterling, so often criticised for being a wasteful finisher, became City's clutch player.
City started the brightest and nearly took the lead on three minutes but Leroy Sane's shot crashed off the post.
Pep Guardiola's side are facing some issues with injuries and suspensions ahead of the Spurs game.
In response to City's goal attempt, Dele Alli also tried one against the opponent's goal post but his shot was deflected off target.
But it quickly became clear that run of three successive defeats wasn't weighing on City.