Blackpool 0 Pompey 1: Half-time reportÂ
The Irishman broke the deadlock on nine minutes as Kenny Jackett's troops dominated the first period at Bloomfield Road.
The Blues almost made the worst start possible, however, when Blackpool's Joe Dodoo crashed a low shot against the post.
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Hide AdOli Hawkins should have given Jackett's men the lead on six minutes but he headed wide from 10 yards.
However, the deadlock was broken by the Blues through Curtis' first goal since completing his switch from Derry City three minutes later.
Hawkins' header caused confusion among the Tangerines defence and the 22-year-old bundled home a right-footed shot from close range.
Curtis could have had a hat-trick before the break after having a goal-bound shot blocked by Ben Heneghan while he cannoned a 25-yard effort off the far post on 37 minutes.
Craig MacGillivray made a few routine saves as the visitors enjoyed most of the possession and chances.