However, Hull sent on Dean Windass at the break and the veteran striker netted twice, either side of what turned out to be the match-winner from the Pilgrims' leading scorer Sylvan Ebanks-Blake.
Argyle made four changes for the all-Championship clash - a dress-rehearsal of the league encounter between the two sides - while Hull manager Phil Brown went even further and brought in seven players.
Hungary international Halmosi engineered Argyle's opening two goals, which came inside three minutes. His free-kick struck defender Damien Delaney and fell for Abdou, who poked the ball past goalkeeper Boaz Myhill.
Another free-kick from the same position, almost immediately afterwards, then curled straight in after Dutch defender Marcel Seip had distracted Myhill.
Recalled Argyle goalkeeper Luke McCormick made a crucial double save just before half-time to deny Stuart Elliott and Hull captain Nicky Barmby, and then spectacularly turned aside a shot from Delaney early in the second period.
Windass pulled one back after a long ball forward was flicked on by Barmby into the path of the 38-year-old, who chipped the ball past McCormick.
Argyle extended their lead when Ebanks-Blake broke down the left and squared the ball for Halmosi, who played it straight back for the 13-goal striker to lash the ball home.
Hull responded immediately when Windass curled in a 35-yard free-kick after Seip had been penalised for fouling Caleb Folan.
Pilgrims substitute Lukas Jutkiewicz, the on-loan Everton striker, nearly put the issue beyond doubt when he ran directly at the Hull defence and fired in a shot that beat Myhill but rebounded off the post.