But Phoenix felt that the final score-line flattered Barnsley, who ran in several tries in the final quarter to make the game safe.
The Castle Park side took an early 3-0 lead with a Johnny Stuart penalty only for the home side to hit back with a brace of tries, one of which was converted, to lead 12-3.
Stuart pegged three points back with a second penalty.
Barnsley stretched their lead to 19-6 with a second converted try before second-rower Greg Neill scored the first of Doncaster’s two tries, converted by Stuart, to make it 19-13 at the break.
Barnsley extended their lead with a penalty early in the second half but the visitors were back in the game when scrum-half Joe Watts went in from a short line-out.
Barnsley got well on top in the final quarter, however, as Phoenix’s earlier efforts started to take their toll.