Rondon marked his 100th Premier League appearance in fine style with a well-taken eighth-minute opener but Jamie Vardy's brilliant 21st-minute volley – his fourth in as many visits to The Hawthorns – hauled Claude Puel's men level.
There was plenty of attacking endeavour from Albion but Alan Pardew's grasp on his job as head coach was made ever more tenuous by Riyad Mahrez's goal after the hour.
Kelechi Iheanacho made that one and the former Manchester City striker was delighted to head home his first Premier League goal for the Foxes, while Vicente Iborra put the finishing touch on a fine away outing late on.
West Brom's involvement in less desirable second-tier competition next term looks altogether more guaranteed as they remain seven points adrift of 19th and eight from safety.
Ben Foster almost conceded in comedic fashion when he fired a clearance against centre-back Ahmed Hegazi that rebounded back towards his own net.
The West Brom goalkeeper scrambled to recover and his side made the most of that let-off by taking an eighth-minute lead – Oliver Burke catching Ben Chilwell napping and crossing to the near post, where Rondon stole in front of Wes Morgan to finish.
Vardy should have levelled when he headed wide from Mahrez's searching delivery but, after Kasper Schmeichel brilliantly tipped a deflected strike from West Brom midfielder Grzegorz Krychowiak against the crossbar, Leicester's go-to attacking duo combined to stunning effect.
There appeared to be minimal danger when Mahrez floated forward a sumptuous pass from just inside his own half. Vardy watched the ball over his shoulder and arrowed a superbly controlled volley low into the right corner.
The England striker thought he had another eight minutes before half-time but was correctly penalised for offside when he prodded home Chilwell's low cross, while a backpedalling Morgan deflected a shot from the marauding Rondon over at the other end.
Foster pawed to safety when Demarai Gray's cross-shot spun off Chris Brunt's knee before Krychowiak trudged off in disgruntled fashion when Pardew sent on youngster Sam Field in the 58th minute.
But it was a Leicester substitute who made a swift and decisive impact, with Iheanacho's cute pass setting up Mahrez to lift a similarly deft finish past Foster.
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.
He could only palm into the net when Iheanacho met Chilwell's chipped cross a couple of minutes later, with West Brom fans heading for the exits in response.
Those who remained saw Iborra rise and power home at the far post form Marc Albrighton's injury-time corner, the imposing Spanish midfielder unchallenged by an Albion defence that seemed physically and mentally shot.
Key Opta stats:
- West Brom have dropped a league-high 21 points from winning positions in the Premier League this season, while gaining just one point from behind in return.
- WBA have now lost six Premier League games in a row – they were last on a longer losing run in league competition between February and April 2003 (seven games), in a season that saw them relegated from the top-flight.
- Jamie Vardy has scored in all four of his Premier League appearances against West Bromwich Albion at the Hawthorns (four goals).
- Riyad Mahrez has provided five assists for Vardy goals this season in the Premier League; the same number as he did in their 2015-16 title-winning campaign and three more than in 2016-17.
- Mahrez has now been involved in 18 Premier League goals this season (10 goals, eight assists) – twice as many as last season (nine – six goals, three assists).
- Vardy (15 goal involvements) and Mahrez (18 goal involvements) are the only players to have been involved in at least 14 goals this season and play for clubs outside the 'big six'.
- Salomon Rondon's goal was his 22nd Premier League strike – since the start of 2015-16, he has scored 12 more goals for West Bromwich Albion than any other player.