Kranjcar, who had got the final touch after Lomana LuaLua's initial shot was saved, looked mystified.
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Lomana LuaLua then curled one into the top corner from the edge of the box seven minutes later.
The Greek champions nearly equalised in the closing stages when Lomana LuaLua's shot was tipped around the post.
Webb blew his whistle even though former Newcastle striker LuaLua appeared to take the ball cleanly from Benoit Tremoulinas.
For their part, Portsmouth seemed happy to play the role of counter-attackers, especially given they had LuaLua's pace to utilise.
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The goal breathed confidence into Holloway's side and it was from another counter attack that LuaLua scored a wonderfully taken second goal.
It was LuaLua who had the first clear shot of the game, although his seventh-minute effort was a mile high of Jens Lehmann's goal.
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Albion needed a left-footed winger after Kazenga LuaLua broke his leg.
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It was a virtuoso opening from LuaLua and on 20 minutes he forced Fulham keeper Antti Niemi into a full-length stop with a dipping 25-yard free-kick.
LuaLua, 25, had promised to refrain from backflips until Pompey were safe from relegation in the Premiership but paid the price for a change of mind.
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Pompey boss Harry Redknapp played a brave hand by replacing defender Lauren with striker Lomana LuaLua, and it immediately added a spark to the visitors' attack.
But Blackpool never looked back once LuaLua latched on to a through ball from Bob Harris before chipping a delightful opener over keeper Scott Davies in the 24th minute.
However, it was the Tangerines who continued to pose the biggest threat with their front four of Thomas Ince, LuaLua and the two Phillips's causing problems every time they broke.
There were times when Campbell looked ill at ease against LuaLua's searing pace, not least when Kolo Toure had to make a last-gasp saving tackle on the DR Congo man.
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LuaLua's four goals in his last four games helped spark Pompey's late battle against the drop but Harry Redknapp's men have since won two of the three games he has missed.
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Phillips hit the post from long range in the 75th minute, but netted his second two minutes later after LuaLua's effort was blocked, then completed his hat-trick nine minutes from time.
But LuaLua was not long out of the game and first Niemi palmed his effort away from a tight angle and then he volleyed wide from Primus' sharp cross just before the break.
Blackpool might have made it 4-0 but Matt Phillips was off-target after being put through by LuaLua and although Lowe shot wide too, Wednesday will return to their League One promotion chase having been outclassed.
Matt Phillips backheeled the ball on to Sylvestre and with the home defence backing away, the French midfielder mirrored LuaLua by curling into the far right corner to book a place in the next round.
Substitute Benjani Mwaruwari forced another fine save with seconds remaining, before LuaLua almost capped a fine performance with the winner with the last kick of the game - only for Niemi to save well once again.
Blackpool broke down the left and when LuaLua's shot was stopped, the ball fell to Matt Phillips on the edge of the area, and he found the bottom corner with a bobbling shot for his 10th of the season.
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