Harvey Barnes put the Foxes into an early lead following a mistake from Robin Koch before Youri Tielemans latched onto Illan Meslier's save from Jamie Vardy's header.
Three minutes into the second half, Stuart Dallas' cross evaded everyone and snuck past Kasper Schmeichel.
However, the hosts' could not turn their possession into goals and Cengiz Under turned provider for Vardy in the second straight away fixture.
In injury-time, Tielemans tucked away a penalty after Mateusz Klich fouled James Maddison.
Foxes' away form best in England
The victory over Leeds means the Foxes are the only side to win their opening four away games of the season, with Tottenham Hotspur winning their first three.
Monday night's performance demonstrated how the club has evolved into a side that performs better when away from the King Power Stadium.
Brendan Rodgers' choice to implement the 3-5-2 formation has now worked wonders at Manchester City, Arsenal and now Leeds. However, when played against West Ham United at home, they were easily beat 3-0.
Despite not impressing as a striker last weekend at the Emirates, Barnes' partnered Vardy up-front in Yorkshire and scored after 141 seconds.
The natural winger's ability to play out wide and through the middle certainly works for Rodgers' side, especially when they are on their travels.
Their next away game is at Liverpool following the international break, but with the Premier League champions not hitting their high standards than they did last season, Rodgers' side will fancy their chances.
Leicester City's squad depth is quite impressive
Ahead of the campaign, worries amongst the Foxes fanbase intensified about the lack of squad depth. With only Timothy Castagne, Wesley Fofana and Cengiz Under arriving, supporters expressed their concerns with the club competition in four competitions.
However, all new signings have slotted perfectly into Rodgers' side and they currently sit second in the league and top of their UEFA Europa League group.
The team that faced Leeds was missing Ricardo Pereira, Caglar Soyuncu, Wilfred Ndidi, Jonny Evans and Castagne. All players who would naturally be starting for the Foxes.
Players that have come in have impressed and now created competition for their places.
A perfect example of this is Nempalys Mendy. The French midfielder struggled to find his spark since his 2016 move from OGC Nice, but this season has seen him show his worth in place of Ndidi.
Against Leeds, he made 33 passes in 41 touches, lost possession zero times and was a key part in how they countered the Whites.
The fact that Leicester are without Soyuncu and Evans, and still defensively solid justifies the strength in depth.
When Youri Tielemans plays well, Leicester City play well
The Belgium midfielder was hugely impressive yet again at Elland Road, scoring twice and pulling the strings in midfield.
His recovery runs were instrumental to City's win and to keeping Pablo Hernandez quiet. As expected, Tielemans dropped deeper in the second half to nullify any Leeds comeback.
Since his loan move was made permanent last summer, a common pattern has developed where when Tielemans plays well, so do the Foxes.
This could be down to many reasons. Firstly, with a fully fit squad, Rodgers often plays Tielemans with James Maddison and Ndidi in a midfield three.
In this three, the 23-year-old is often the box-to-box midfielder whilst Maddison ventures more into a free role and Ndidi dropping into the defence.
At Elland Road, Tielemans was alongside Mendy and Dennis Praet in midfield, switching with the later in advancing forward.
His first goal demonstrated him fulfilling the role of player further forward, where he was in the right place at the right time to slot the ball home.
However, when Tielemans has an off day, it ripples out to the rest of the squad. With him often giving away the ball too easily or failing to trackback.
This season has seen him impress the majority of the time and is really showing why the club paid the £30million for him.