Rondon rose impressively in the 89th minute, arriving to nod in Chris Brunt’s free-kick and complete Albion’s recovery from a two-goal deficit at the Hawthorns.
But bottom of the table West Brom still look set for relegation from the Premier League as they are eight points from safety with only three games left.
Liverpool remain third, three points behind second-placed Manchester United.
Jurgen Klopp’s side had seemed firmly in control as Salah equalled Ian Rush’s Liverpool record of scoring in 32 different games in a single season and collected his 31st league goal of the campaign, his 41st overall.
Egypt winger Salah tied the Premier League record of most goals in a 38-game campaign, joining Alan Shearer (1995-96), Cristiano Ronaldo (2007-08) and Luis Suarez (2013-14).
He also equalled Suarez’s Liverpool record for most goals in a Premier League season.
Earlier, it was Danny Ings, a player whose Liverpool career has been blighted by injuries since moving from Burnley, who was the centre of attention with his first goal in 930 days.
Ings was preferred to Roberto Firmino, one of five key personnel rested by Klopp with an eye on Tuesday’s Champions League semi-final first leg with Roma, and the former England international wasted little time in justifying his manager’s faith.
Sadio Mane worked a short corner with James Milner, crossing into the six-yard area where Georginio Wijnaldum had space to control the ball into the path of Ings who drove home convincingly.
It was Ings’ first goal since scoring against Everton in October 2015, shortly after his move to Anfield, and his celebrations indicated the obvious relief felt by a player who has badly injured the cruciate ligaments in both knees in the intervening years.
– Anxious finale –
More importantly, the goal put Liverpool ahead in a game Klopp badly needed to win in his quest to ensure his side finishes the season in the top four to guarantee Champions League football next term.
Klopp has insisted that a top-four finish remains as much a priority as reaching the Champions League final and a run of just one defeat in their last 15 games in all competitions testifies to the German’s intent.
On this occasion, Liverpool seemed to be as good as over the finishing line on 71 minutes when Salah moved five goals clear of Tottenham’s Harry Kane in the race for the Premier League’s Golden Boot award.
Firmino headed on a long punt from Loris Karius with Alex Oxlade-Chamberlain taking up the running before playing in Salah who finished clinically by lifting the ball over the keeper from eight yards.
But Klopp was left to face an anxious finale when Albion pulled a goal back on 78 minutes.
Brunt’s corner was headed back across goal by Jay Rodriguez and, after a Craig Dawson shot had been saved, Jake Livermore rammed home the loose ball.
The balancing act, of ensuring his side continues to pick up league points while preparing for their Champions League campaign, has not been an easy one and Klopp’s team selection carried with it a degree of risk.
Not that the early going was too problematic for Liverpool as Salah saw a shot deflected behind off Livermore, Ings headed wide from Milner’s cross and Salah planted a 20-yard free-kick over.
But Albion, fresh from their surprise victory at Manchester United last weekend, grew into the game and Rodriguez came close to converting a James McClean cross before the interval, foreshadowing the late comeback that gave Liverpool a shock before their European adventure.