In what was also the fourth successive Mercedes one-two, and fifth win in five races for the dominant constructor, Hamilton took the chequered flag a mere 0.6 of a second ahead of his rival.
In a nail-biting finish to what had been a largely uneventful race, Rosberg piled pressure on Hamilton by slashing the Briton's lead over the last six laps and looming ominously in his mirrors.
Hamilton, who now has 100 points to Rosberg's 97 after his 26th career victory and leads the standings for the first time since 2012 when he was at McLaren, sounded increasingly anxious in radio traffic but held on for his first win in Spain.
"I wasn't fast enough really today, Nico was quicker," the 2008 champion said during the podium interview. "Fortunately I was able to keep him behind."
Rosberg, who declared himself "a bit gutted" to finish second again and whose subdued body language alongside Hamilton on the podium more than backed that up, felt he would have got past with one more lap.
"Lewis did a great job the whole weekend, just that little bit ahead," added the German ruefully.
Daniel Ricciardo was third for champions Red Bull in the first podium finish of his F1 career after being stripped of his second-place for a fuel irregularity in his home season-opener in Melbourne in March.
"We did not have the pace on Mercedes... it is really nice to be on the podium and I am sure I will get to keep it this time," said the smiling Australian, who had started third.
"A lonely third was not a bad result in the end".
VETTEL FOURTH
Quadruple world champion team mate Sebastian Vettel, who started 15th after a five-place grid penalty for a gearbox change, ended a weekend of setbacks with a strong fourth place.
The 26-year-old German had arrived at the first European race of the season with a different chassis to the previous four grand prix, in which he had made just one podium appearance, but Red Bull remained an age away from Mercedes.
Ricciardo, as the best of the rest, crossed the line a massive 48.3 seconds behind Rosberg with Mercedes again in a class of their own and lapping all but four cars.
Ferrari's Kimi Raikkonen was one of those passed by Hamilton, finishing seventh and just behind Spanish team mate Fernando Alonso - last year's winner - in sixth.
Finland's Valtteri Bottas took fifth place for Williams, while Brazilian team mate Felipe Massa sank from ninth at the start to 13th at the finish.
Frenchman Romain Grosjean handed Lotus their first points of the season with eighth place, ahead of Force India's Mexican Sergio Perez and Nico Hulkenberg in ninth and 10th respectively.
Only two drivers retired, Toro Rosso's Jean-Eric Vergne and Caterham's Kamui Kobayashi, in a 66 lap race that testified to the surprising reliability of the cars in the new V6 hybrid turbo era.
Venezuelan Pastor Maldonado, who crashed in qualifying and started last for Lotus, was handed a five second stop/go penalty for causing a collision with Caterham's Marcus Ericsson.
(Reporting by Alan Baldwin, editing by Pritha Sarkar)
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