Raikkonen took the lead for good on lap 43 of 58 in a race that had seven different leaders, and had the luxury of driving conservatively in the closing laps while Ferrari's Fernando Alonso and Red Bull's Sebastian Vettel scrambled in vain to keep up.
The Finn needed only two pit stops compared to three stops for each of the six men who followed in his wake, and he became the 15th driver in F1 history to record 20 grand prix wins.
"Our plan was to do two stops and though it's always difficult in the first races to know when to stop and not go too early, we got it exactly right," Raikkonen said.
"We followed the plan and it worked out perfectly for us. I could save the tires and go fast if I needed. It was one of the easiest races I have done to win and hopefully we can have many more of these races."
Alonso looked like he had a chance when he trailed Raikkonen by 6.2 seconds with 12 laps to go, but could not make up ground. Still, he was satisfied with where Ferrari stands compared to the poor performances to start last season.
"I am extremely happy," Alonso said. "We had a difficult start of season two years ago and last year, too, and this year is very different. We feel much more comfortable, the car is responding well and we have a good season ahead of us."
Pole sitter and three-time reigning world champion Vettel was third in a Red Bull. He was forced to pit after just seven laps due to worn super-soft tires and never threatened thereafter.
"The first few laps were okay but then the tires were falling apart and we could not go as far as other people," Vettel said.
"We have to admit sometimes that other people are faster than us but it's a long season so we have some good points to start with and we have no reason to be disappointed."
While Vettel was accentuating the positive, the race performance was a disappointing one, and the rapid tire degradation is a headache for a team which had precious few reliability issues over recent years.
Ferrari's Felipe Massa was fourth in an encouraging performance that indicated he had carried the strong form of late 2012 into the new campaign.
Lewis Hamilton was fifth in his first race for Mercedes, having to ditch his plans for a two-stopper and switch to three because of tire degradation. The Mercedes race pace was underwhelming and the dominant performances of preseason testing are already a distant memory.
Mark Webber of Red Bull was sixth. The Australian local favourite qualified second on Sunday morning — qualifying was postponed from Saturday due to heavy rain — but yet again made one of his frustrating slow starts off the line, was seventh after lap one, and still has not finished on the podium in his home race in 12 attempts.
Force India pair Adrian Sutil — who twice led the race and was the man overtaken by Raikkonen for the lead — faded to seventh as he struggled on the super-soft tires in the closing stages, and finished ahead of teammate Paul di Resta. McLaren's Jenson Button and Lotus' Romain Grosjean rounded out the top 10.
While Lotus was acknowledged even in preseason testing to have a pace comparable to the likes of Red Bull and Ferrari, there was a nagging doubt whether it would have the depth of financial resources to challenge its bigger rivals throughout the season.
Raikkonen was not yet eyeing off the championship but was hoping more money would arrive to sustain a challenge.
"It's not going to be as easy for us," Raikkonen said. "We have the people and the tools to make it, but the money is the big part of the whole thing.
"Last year we did pretty well on the money. If we can get more money it will help and a better chance for fair play against the big teams."
McLaren had been off the pace of its rivals throughout practice and qualifying, paying the price early in the season for a radical overhaul of the car in the hope of having more development upside in the second half.
That continued in Sunday's race with Jenson Button an uncompetitive ninth and Sergio Perez leaving empty handed in his McLaren debut, finishing 11th.
Mercedes' Nico Rosberg, who set the fastest time in first and second qualifying sessions, retired on lap 27 due to an electrical failure, while Sauber driver Nico Hulkenberg did not even start the race due to a fuel-system problem.