The Blues’ seventh clean sheet in eight games was also key to the victory on a difficult playing surface that had been used to host an NFL game on Sunday.
A minute’s silence was impeccably observed before kick-off following the Leicester City helicopter tragedy, and for remembrance to those lost in armed conflict.
And soon after the match started, a poignant moment arrived via the Blues’ opening goal.
A superbly subtle stop-start feint by Sterling beat Trippier for a second time before he crossed for Mahrez to finish – the former Leicester man pointing to the heavens in recognition of a traumatic time for everyone connected with the east midlands club.
That early goal set up a pulsating game, with City bossing possession but passing up a number of chances despite typically silky build-up play.
With the advantage just one goal, a thread of tension ran through the game and had boss Pep Guardiola up on his feet and animated in the away technical area.
In the end, City’s back-line solidity helped secure the points; we are on the best defensive run in the Catalan manager’s City spell so far.
MATCH STATS: See full player analysis here
On his 200th Premier League appearance Sterling produced a dazzling display down the left flank, full of invention and verve, with one nutmeg setting Sergio Aguero through on goal only for his shot to flash wide.
There was a warning at the other end soon after when Harry Kane lashed an effort inches over from distance, but for the most part City held the upper hand.
Despite a less-than-perfect surface – the result of Sunday’s NFL clash between Philadelphia Eagles and the Jacksonville Jaguars – the Blues were linking play well in Spurs’ half.
Bernardo and David Silva used their prodigious technical ability to minimise the pitch impact, with Mahrez going close to adding a second only for Hugo Lloris’ sharp one-handed save denying him.
Elsewhere Fernandinho was at his combative best, tracking back brilliantly to intercept one Spurs chance and constantly disrupting the home side's attacking intent.
When Kane did grab a one-on-one opportunity, Ederson charged out to make a crucial tackle at the striker’s feet.
City had a good chance to double the lead early in the second half but after Bernardo rolled the ball across the box, Silva couldn’t get his shot away and Sterling’s effort was blocked.
Aguero shot too close to Lloris when the next chance arrived, before a vicious volley from the Argentinian forced another parried stop.
Spurs had a great chance to level late on but, arguably in part due to a bobbling ball, Erik Lamela put his shot over the bar.
City held on for a remarkable fourth Wembley win in 2018, more points picked up away at a title rival, and return to the top of the Premier League table.
Star man - Riyad Mahrez
The former Foxes winger showed great courage to play and performed admirably throughout, producing the game's decisive moment for his second goal in two Premier League games.
"Lamela had a big chance and we missed a lot (of chances). You cannot expect to score a lot of goals against Spurs.
"Sometimes, we made mistakes. The pitch was so complicated.
"We played against of the most physical teams I've ever faced. They have incredible physicality and on this pitch, it was so complicated.
"We missed some goals and let them turn and they are so good."
The team set up in a powerful four-five-one formation, with right-back Kyle Walker restored to the starting line-up for the first time since picking up a knock on international duty earlier this month. In-form centre-back Aymeric Laporte continued his ever-present record for the season.
In midfield, Guardiola went with the Bernardo-David Silva nexus, with De Bruyne on the bench following his first start after injury last week against Shakhtar Donetsk. Fernandinho occupied his usual anchor role, with Mahrez and Sterling providing width, the latter notching up his 200th Premier League appearance.
City have four home games in quick succession now as follows:
Fulham, Thursday 1 November, kick-off 19:45 (League Cup)
Southampton, Sunday 4 November, kick-off 15:00 (Premier League)
Shakhtar Donetsk, Wednesday 7 November, kick-off 19.45 (Champions League)
United, Sunday 11 November, kick-off 16:30 (Premier League)