They missed many chances to further extend the scoreline but headed into halftime with a twogoal advantage.
In the 84th minute, Gndoan missed a chance to score his treble of the match but saw his penalty kick saved by goalkeeper Joel Robles.
But Rodrigo would score less than 60 seconds after to net a consolation for Sam Allardyces side.
With three rounds of matches excluding outstanding fixtures left, City lead the table as they edge closer to another league title which will see Pep Guardiolas side match the feat achieved by only Alex Ferguson
The Scottish legendary manager won three consecutive league titles twice with Citys archrivals Manchester United.
However, the result might have a longstanding effect on Leeds United who are pushing for survival a win for either 18thplaced Nottingham Forest or 19thplaced Everton in their own fixtures will see the Whites drop down into the relegation zone.
Liverpool vs Brentford
Meanwhile, Liverpool are now one point shy of the top four thanks to a narrow 10 home win over Nigerias Frank Onyekas Brentford.
Mohamed Salah scored the only goal of the game which was the former Chelsea stars 100th league goal for the Reds at Anfield.
The Egyptian star netted the landmark goal in the 13th minute.
But neither of them were able to score again throughout the remainder of the fixture.
The only time the visitors managed to find the back of the net came in the second half but Bryan Mbeumos goal was ruled out for an offside.
The Reds move just one point adrift of fourthplaced Manchester United who are on 63 points but have played two games less than Liverpool as the Champions League qualification race remains widely opened.
Bournemouth vs Chelsea
After seven games, Chelsea were finally able to record their first win of the second reign of Frank Lampard across all competitions with a 31 away victory at Bournemouth.
Following six straight defeats, goals by Conor Gallagher, Benoit Badiashile and Joao Felix were able to give Frank Lampard a sigh of relief after a tough start to second life at Stamford Bridge.
It was Chelseas first win since March and Lampards first win in his last 10 managerial matches.
Gallagher put the Blues ahead through a header barely 10 minutes into the match but the hosts would soon hijack possession which resulted in Bournemouths equaliser thanks to Matias Vinas perfect curler in the 21st minute.
The scoreline was maintained by both teams until the tailof the second half.
In the 82nd minute, French starlet, Badiashile returned Chelsea back into the lead before Atletico Madrid loanee, Felix sealed the needed victory for the Blues four minutes later.
Thanks to the win, the Blues move a position up from 12th to 11th with 42 points which means irrespective of the result from Chelseas remaining matches, they would not get relegated from the English topflight division.
Tottenham vs Crystal Palace
Harry Kanes goal helped Tottenham pip Crystal Palace 10 in a lowclass London derby as the Lilywhites returned to winning ways after three defeats and a draw in their previous four league matches.
Kanes firsthalf stoppagetime goal secured all three points for Spurs the goal was the England internationals 209th Premier League goal which placed him second on the alltime EPL top scorers chart ahead of Manchester Uniteds legend, Wayne Rooney(208)
Full Saturdays matchday 35 results
Manchester City 2 vs 1 Leeds United
Liverpool 1 vs 0 Brentford
Bournemouth 1 vs 3 Chelsea
Tottenham 1 vs 0 Crystal Palace
Wolves 1 vs 0 Aston Villa