The team's victory celebration, however, was cut short when a smoky fire erupted in its garage area following the race.
Pole-sitter Maldonado secured his first career Formula One victory after fighting off a challenge by Spain's Alonso, who trailed by less than 1 second in the later stages of the race.
But he held on to become the first-ever Venezuelan to win a Formula One grand prix event, besting Alonso by 3.2 seconds at the finish.
The result handed Williams its first checkered flag since the 2004 Brazilian Grand Prix -- the last year Juan Pablo Montoya drove for the team before leaving for McLaren.
Finishing a close third was two-time Spanish GP winner Kimi Raikkonen, followed by Romain Grosjean and Kamui Kobayashi.
Defending Spanish Grand Prix champion Sebastian Vettel ended in sixth after serving a drive-through penalty for failing to slow down during a mid-race caution.
After the race, the Williams celebration was interrupted when a fire erupted in its garage area at Barcelona's Circuit de Catalunya.
Initial reports indicated no serious injuries but personnel from Williams and Force India were given medical treatment at the track's medical center.
The fire apparently started in one of Williams' cars and produced thick smoke in the pit lane area, causing extensive damage to the team's garage equipment and to driver Bruno Senna's car.
Britain's Sky Sports reported witnesses as saying there was an explosion in the back of the garage as team owner Frank Williams was delivering a victory speech to the team.