On the second weekend of the new campaign, Carlo Ancelotti’s side fell behind to Grady Diangana’s early goal at Goodison Park.
But Calvert-Lewin equalised and James Rodriguez put Everton ahead with his first Premier League goal before Albion imploded.
Kieran Gibbs was dismissed for pushing James in the face in first half stoppage-time, a rash reaction that prompted him to issue a post-match apology taking “full responsibility” for his mistake.
Then Albion boss Slaven Bilic was sent to the stands after storming onto the pitch for a furious rant at referee Mike Dean.
Matheus Pereira equalised for Albion after the interval, but Michael Keane restored Everton’s lead and Calvert-Lewin sealed the points with his second and third goals.
Ar 23, Calvert-Lewin is the youngest Englishman to score a Premier League hat-trick for Everton.
After a summer spending spree, Ancelotti is under pressure to deliver a big improvement on last season’s 12th place finish and the early signs are promising.
Having beaten Tottenham in their opening game last weekend, Everton have started a Premier League season with consecutive victories for the first time since 2012-13.
Calvert-Lewin already has four goals and Colombia midfielder James, making his first home appearance since his £12 million ($15.5 million) from Real Madrid, looks a quality addition.
“Of course today Dominic was the top scorer but also Richarlison did really well, the combination in front was good,” Ancelotti said.
“They are supported by James, who is doing really well. I’m satisfied in front, we have to do better at the back.”
If West Brom are to avoid an immediate return to the Championship, they will have to improve their defence rapidly after shipping eight goals in successive defeats.
– Free-scoring Leeds –
At Elland Road, promoted Leeds were involved in another eye-catching encounter in their first top-flight home match for 16 years.
After losing 4-3 at champions Liverpool on the opening weekend, Helda Costa fired Marcelo Bielsa’s free-scoring side ahead in the fifth minute, blasting home from a tight angle following Kalvin Philips’ corner.
Fulham striker Aleksandar Mitrovic equalised from the penalty spot in the 35th minute after a foul on Joe Bryan.
Bryan was penalised himself for his shove on Patrick Bamford and Mateusz Klich restored Leeds’ advantage with a 40th minute spot-kick.
In the 51st minute, Klich’s fine pass into the area carved Fulham’s defence open and Patrick Bamford steered a right-footed finish into the bottom corner.
Leeds struck again six minutes later with a superb second goal for Costa, who slammed home following Bamford’s superb run and cross.
Fulham pulled one back in the 62nd minute through Bobby Decordova-Reid and Mitrovic’s towering header four minutes later set up a tense finale, but the promoted Cottagers fell to a second successive defeat.
Leeds’ opening games have seen 14 goals, which is the most for a top-flight side’s first two matches since Wolves in 1962-63.
Later on Saturday, Manchester United play their first game of the season against Crystal Palace before Arsenal host West Ham.