Hamilton and new team-mate Charles Leclerc both managed to get ahead of Russell in a stunning start for Ferrari, with Russell and his team-mate Kimi Antonelli instead being demoted to sixth and seventh after lap one.
Mercedes have also been concerned about their lack of race pace this weekend, and their difficulties managing their tyres in hot conditions, making the start crucial to their chances.
Meanwhile, nearer to the front, Max Verstappen produced another brilliant lap one overtake to get ahead of McLaren's Lando Norris, as Oscar Piastri got away well to lead his two championship challengers.
Hamilton shines at the start, but struggles continue
While seven-time world champion Hamilton managed to outqualify Leclerc for only the second time since becoming team-mates with the Monegasque star, his race pace was clearly suffering compared to the other Ferrari.
Hamilton's stunning lap one had put him right behind Norris in the battle for the final podium slot, but that gap soon started to open up.
Hamilton was five seconds behind his fellow Brit after nine laps, with Leclerc tucked up right behind his team-mate, prompting Ferrari to make a change in the order of their two cars.
Ferrari issued team orders to allow Leclerc to go and chase after the top three cars, highlighting Hamilton's early season struggles once again.
The Spanish GP was all set for a battle between the three championship protagonists at the front, after an enthralling opening few laps.