Sunderland, who were in the Premier League two years ago, showed little attacking ambition and had to rely on three vital saves from goalkeeper Jon McLaughlin to see them through to the final while hosts Portsmouth also hit the bar.
The north-east club, who have been English champions six times, will face either Charlton Athletic or Doncaster Rovers in the final at Wembley on May 26 for the right to be promoted to the Championship, England's second tier.
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Sunderland spent 10 consecutive seasons in the Premier League before going down in 2017 and were then relegated to the third tier of English football.
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