They won 32-20 in Penzance to overturn a narrow first leg defeat and set up a last eight tie with Coventry – with the first leg at Castle Park on Saturday.
During an outstanding performance at Mennaye Field, two tries by flanker Sam Hudson and one each by hooker Will Holling and backs Maliq Holden and Mark Best ensured that Doncaster won 56-46 on aggregate.
Their win by five tries to three in a highly competitive and entertaining contest was also boosted by two conversions from fly half Billy McBryde and a late penalty from his replacement Sam Olver.
Knights head caoch Steve Boden, whose side finished second in the league, was thrilled with his team’s performance.
“It was a huge team effort, the best all year,” he said.
“In many ways, it was the complete team performance. Although we missed three opportunities in the first half, in the second the bench had a big impact.
“Our attacking and scrums were good, we were unlucky to be down 15-12 at half time and some of the boys stood out and told me why they should have been starting in previous games.”
Pirates led by 10-0 at one point but Doncaster’s forwards fought back strongly.
Following Hudson’s tries on 28 and 37 minutes, Knights increased their pressure to dominate the second half when Holling, Holden and replacement centre Best smashed the Pirates’ defence to go 29-12 ahead.
A yellow card for second row Ben Murphy meant that Doncaster finished with only 14 players.
But this handicap was overcome and an excellent display was completed when Olver’s 79th minute penalty was kicked accurately.
Pirates: AJ Cant, Wedlake, Wyatt, Tucker, Sirker, Bazalgette, Dawson, Walker, Channon, Petch, Teague, Cutmore, Bolwell, Gibson, Duncan.
Knights: Davey, Evans, Edwards (Best 64), Strachan, Holden, McBryde (Olver 52), Green (Wheeldon 77), Wrafter, Holling (Edgson 66), Denman (Paul 45), Kelly, Peters (Murphy 50), Hudson, Smith, Volpi.
Referee: Dan Jones