With coaches able to substitute players in and out, Watson did not play a role with the bat in New Zealand's second innings.
Although Australia were set 206 for victory with 66 overs left on the third day, the chase looked to be straight forward.
However, their pursuit was far from smooth sailing, losing three of their top-order early on to be 38 for three.
It took an unbeaten eighth wicket partnership worth 32 to thwart New Zealand's hopes.
Watson was not required much with the ball in the final innings, only being allowed one over as again nine bowlers were used.
The series now turns to the one-dayers, with the first of three 50-over matches beginning April 4 at the Bert Sutcliffe Oval in Lincoln.