The Baggies travelled to the King Power Stadium - where they had never previously lost - knowing time is rapidly running if they are to avoid an instant return to the Championship.
But the opening 45 minutes saw them outclassed with Jamie Vardy, Jonny Evans and Kelechi Iheanacho on target in a half completely dominated by Brendan Rodgers side.
The Baggies improved marginally after switching formation at the break.
But Leicester still cruised to their win with Sam Allardyce's side never once looking like they would take something from the game.
The result leaves Albion, who face rivals Villa on Sunday, nine points from safety with just six games remaining.
Allardyce opted to stick with the team that secured a comfortable victory over Southampton when naming his starting line-up.
Opting for a 4-2-3-1 system, Mbaye Diagne was the lone centre-forward with Matheus Pereira in the number 10 role and Callum Robinson and Matt Phillips out wide.
In central midfield, Ainsley Maitland-Niles - who has been a transfer target for Leicester in the past - was joined by Okay Yokuslu.
Leicester lined up in a 3-4-1-2 formation that saw the in-form Iheanacho partner Vardy in a dynamic front two.
James Maddison occupied the space just behind them with Luke Thomas and Timothy Castagne deployed as wing-backs.
In what proved a blistering opening few minutes, both teams had glorious chances to open the scoring.
It was the hosts who threatened first when Conor Townsend inexplicably dallied on a long-ball forward.
Seemingly caught in two minds on how to make a clearance, that hesitancy allowed Iheanacho to first win the ball and then charge clean through on goal.
Full of confidence it seemed certain the striker would round Sam Johnstone to score.
But the goalkeeper did really well to first force him wide before then blocking his shot with legs.
Albion went straight up the other end with Phillips sending in a cross which Wesley Forfana headed straight to Pereira who was around 10-yards from goal.
He then squared for Diagne who simply had to side-foot the ball home.
But incredibly, the striker failed to make any real contact with the ball - with that miss granting Leicester a huge let-off.
The game continued to be played at a high tempo from that point on but as the clock ticked past the 20-minute mark, Leicester began dominating possession.
And a frantic 10-minute spell then saw the hosts score three times - when they should really have scored four.
Rodgers' side opened the scoring when a brilliant Youri Tielemans pass allowed Timothy Castagne to get in behind the Albion defence.
He then squared for Vardy who emphatically fired past Johnstone for his first goal in two months.
Just three minute later the hosts had doubled their lead when Tielemans's corner was flicked on allowing Evans to power a header into the roof of the net.
Albion, all of a sudden, were at sixes and sevens with the team looking a shadow of the one that has been so competitive in recent weeks.
And Leicester came a whisker away from grabbing a third when Maddison again switched the play to Catasgne who charged into the box before smashing a low drive against the post.
Albion were now struggling to get any foothold on the game with their midfield nonexistent.
A rare breakaway saw them win a corner from which Pereira delivered an inswinging cross which hit the crossbar.
But Leicester were rampant and they made it 3-0 in the 36th minute when Vardy raced past O'Shea to enter the box.
The former England international then sent in a low cross which Iheanacho controlled before firing in.
Incredibly, the hosts should have grabbed a fourth before the interval.
Another exquisite cross-field ball from Maddison found Castagne who nodded the ball onto Iheancho.
The former Man City striker then produced a wonderful piece of skill to take the ball away from Kyle Bartley.
But from 10-yards he then fired over when he really should have scored.
Albion made a change at the break with Semi Ajayi replacing Robinson.
That meant the Baggies switched to the 3-5-2 system they started with when Allardyce decided to match Chelsea - with Ajayi joining O'Shea and Bartley at the heart of the defence.
Phillips moved into central midfield alongside Maitland-Niles and Yokuslu while Pereira partnered Diagne up front.
The change did make the Baggies look more solid in the opening stages of the second-half
But it was still Leicester who continued to look the more dangerous of the sides with Iheanacho and Maddison playing a clever one-two that ended with the striker seeing a shot deflect narrowly over.
Allardyce subbed Diagne for Hal Robson-Kanu on the hour mark.
But Rodgers' side continued to dominate all over the park.
And with one eye potentially on the derby at Villa, Allardyce took off Pereira with around 20 minutes to go with Karlan Grant replacing him.
Leicester almost grabbed a fourth late on when Iheanacho saw a free-kick 20-yards out well saved by Johnstone.
But in truth, the entire second-half was a procession with Albion never looking like getting back into it while Leicester were able to cruise to victory thanks to their excellent first-half display.
Leicester (3-4-1-2): Schmeichel, Fofana (Albrighton 62), Soyuncu, Evans, Castagne, Tielemans, Ndidi, Thomas, Maddison (Perez 72), Iheanacho, Vardy (Praet 84).
Subs not used: Ward, Amartey, Under, Choudhury, Pereira, Mendy.
Albion (4-2-3-1): Johnstone, Furlong, Bartley, O'Shea, Townsend, Yokuslu, Maitland-Niles, Phillips, Pereira (Grant 73), Robinson (Ajayi 46), Diagne (Robson-Kanu 61).
Subs not used: Button, Peltier, Livermore, Sawyers, Gallagher, Diangana.