The engineers voted overwhelmingly in favour of strike action, with 98% in favour, and unanimously voted for industrial action short of a strike over plans to transfer a eight jobs to Universal Tyres.
It is understood that the company has agreed signing a deal with Universal Tyres to allow time for further talks looking at alternative proposals.
Had the strike gone ahead, the row over outsourcing risked escalating after Unite announced a ballot of the wider dock workforce on industrial action over the issue.
Unite has about 1,900 members at the UK's busiest container port, including the 116 engineers.Unite has agreed to take no action on the result of that postal ballot - which was due to open on December 24 and close on January 14 - while talks take place.
However, both sides could revert to their previous positions if the talks aren't successful.
Unite regional officer Miles Hubbard described it as "a step forward".
"Unite is pleased the company has taken this pragmatic position. Talks will continue in the new year."
They "very much hope to reach a resolution" and hope to reach agreement on outsourcing in the long term.
"In the meantime, we reserve our position if the talks break down."
The port employs around 2,500 staff in total. Port boss Clemence Cheng wrote to the workforce after the strike was announced, and again after the ballot of the wider workforce, warning that the port faced "a number of headwinds", and that strike action risked damaging the business.