Despite their recent poor form, West Brom had signs of optimism just 8 minutes into the game when Oliver Burke displayed his physical attributes against Chilwell before crossing to Rondon who finished easily.
Stranded at the bottom of the points table, finding it tough to get anywhere near safety, Alan Pardew's West Brom look destined to face the drop this season.
Leicester made it 4-1 in injury time when Vicente Iborra headed home from a corner.
In the eighth minute, the home side was lifted when Rondon opened the scoring after getting on the end of Oliver Burke's good run and cross from the right. Baggies 'keeper Ben Foster had to be alert when Chris Brunt deflected a Demarai Gray cross towards his own goal.
Pardew introduced Jay Rodriguez on a salvage mission for Albion but Leicester continued to look the sharper and more incisive attacking force - Foster denying Vardy impressively with his legs in the 74th minute.
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With no win in their last six league games, they are seven points off safety and will need to start picking up some points to have a chance of avoiding relegation this season.
Iheanacho then got in on the act himself to make it 3-1 and in stoppage time Iborra added another to rub further salt into West Brom's festering wounds.
Since last March, West Brom have won three of their 39 Premier League games.
Puel was full of praise for Vardy after his goal which made it level in the first-half.
In the other Premier League games on Saturday, Everton beat Brighton 2-0 at Goodison Park as Newcastle thumped Southampton 3-0 at home.
Claude Puel's men came back from a goal down to win West Bromwich Albion on Saturday.