It is the start of a process expected to take several months.
Poor weather halted the operation earlier this week, but since yesterday salvors have made the most of good conditions in the Bay of Plenty, Maritime New Zealand salvage manager Kenny Crawford said.
"Obviously getting the first container off is a milestone for the operation, but there is still a very long way to go. The removal process will take time as, for safety reasons, each container needs to be lifted separately. Each will also present its own challenges, depending on its position on the vessel and how badly damaged it is," he said.
So far, 118 electronic transponders have been fitted to the containers sitting most precariously on deck, which will allow them to be tracked should they topple overboard.
A further 102 transponders are being prepared and fitted.
"We've also achieved another milestone in emptying port fuel tank number five, which can now be classified as empty of oil," Mr Crawford said.
Nineteen of the 88 containers that fell off the ship in bad weather last month have been recovered.
Once recovered from the ship, the containers will be decontaminated and taken to port.
Beach warning
Bay of Plenty beachgoers are warned to take caution this weekend, as oil continues to resurface on the shore and clean-up operations continue.
Beach access restrictions were put in place from Mt Maunganui to the Maketu Estuary to allow response teams and volunteers to clean up oil that washed up from the stricken ship Rena, which ran aground on the Astrolabe Reef near Tauranga last month.
The restrictions were lifted yesterday (Wednesday) but authorities are warning that clean-up operations are not yet over and care still needs to be taken.
Maritime New Zealand national on-scene commander Mick Courtnell said weathered oil may continue to resurface for some time.
"It is important for the public to understand that - if they choose to head down to the beach this weekend - things are not the same as they were, and they will need to take care."
Beachgoers and swimmers were advised to exercise caution, avoid oil on the beach or in the water, and to supervise children.
The oil was a minor health risk and should be washed off with soapy water.
A navigational safety exclusion zone also remains in place, with boat ramps within the exclusion boundaries at Papamoa East, Bell Rd and Maketu remaining closed.
Public health authorities have advised the public not to collect shellfish, crabs, kina and seaweed, while a rahui from local iwi prohibiting the collection of kaimoana between Bowen Town Beach and Maketu was also in place.
Beach restrictions remain in place on a stretch of Papamoa Beach, east of Harrison's Cut to Alexander Place, and at Maketu Spit.
Maritime New Zealand and local councils were supporting a community 'adopt-a-beach' initiative that aimed to mobilise clean-up volunteers to monitor high-use areas of beach.
"This is a brilliant opportunity for the community to take ownership of the beach and make a huge contribution to its recovery. I encourage locals to get in touch and be part of the amazing volunteer effort we have seen so far," Mr Courtnell said.