Watson and Salisbury secured a 5-7 6-3 10-8 victory over Belgium’s Sander Gille and Nadiia Kichenok of Ukraine.
The match had begun on Monday, but rain had led to a premature hault.
The British duo resumed the contest yesterday a set down but 5-3 up in the second.
They were soon back on level terms.
Watson and Salisbury then came out on top in a gruelling decider and go on to face Poland’s Jan Zielinski and Su-Wei Hsieh of Taiwan in a contest scheduled to take place early this afternoon.
The mixed doubles final has been pushed back from Thursday to Sunday due to a backlog of matches.
