With the tie delicately balanced from the first leg at 2-2 Fulham knew that a goalless draw or a 1-1 scoreline would be good enough to qualify for major European competition for the first time in their history.
The Premiership outfit got off to a perfect start opening the scoring after just 12 minutes through the in-form Inamoto.
The Italians dragged themselves back into the contest when Tomas Locatelli levelled things up in the 34th minute.
Fulham restored their advantage just two minutes into the second half through a fine strike from Inamoto.
Inamoto then completed his hat-trick just three minutes later to make the game safe for Fulham with a simple tap-in to make sure of their place in Friday's draw for the Uefa Cup first round.
The Japanese midfielder never really got a look-in at Arsenal last season, but he has proved to be an inspirational signing for Jean Tigana hitting four goals for his new side.
The result justifies Fulham's decision to compete in the much-maligned competition and can now look forward to battles with some of Europe's big boys in the Uefa Cup.
Two late goals helped Stuttgart earn a place in the Uefa Cup as they overcame Lille 2-0 at The Gottlieb-Daimler Stadion on Tuesday night to record a 2-1 overall aggregate win over the French side.
Trailing 1-0 from the first leg in France, Stuttgart knew they faced an uphill task to reach the Uefa Cup first round.
The home side missed a great chance to bring the tie level three minutes into the second half when Bulgarian international Krassimir Balakov failed from the penalty spot after Stephane Pichot had been sent-off in the build-up to the penalty award.
Midfield playmaker Balakov made up for the miss with the crucial equalising goal nine minutes from time.
It seemed that the game was destined for extra-time until Stuttgart netted a dramatic winner two minutes from time through Kevin Kuranyi to seal their place in the Uefa Cup.
Malaga also booked their place in the Uefa Cup first round with a 2-1 aggregate win over Spanish rivals Villarreal after a bad tempered 1-1 draw in the second leg on Tuesday night.
The home side were in the driving seat after a first leg 1-0 win away from home and they doubled their overall lead through Miguel Angel Roteta just after the half hour mark.
Carlos Reina gave the visitors some hope with an equaliser after 65 minutes, but the game turned ugly in the closing minutes.
Both sides were reduced to ten men a minute from time with Martin Palermo seeing red for the visitors and Jose Josemi receiving his marching orders for Malaga.
Villarreal's misery was compounded when Reina was dismissed for his second bookable offence in stoppage time.
