Ragged Pompey surrendered a two-goal first-leg advantage inside 32 minutes as Guimaraes took advantage of sloppy defending to force extra time.
Brazilian striker Douglas shot home in the 19th minute after a corner skimmed off Sol Campbell's head - and England goalkeeper David James was beaten again when rooted to his line, by a 35-yard shot from midfielder Joao Alves.
But Crouch made no mistake for his 100th goal in club football when nodding in at the far post from Glen Johnson's delivery in the 104th minute - and he then added a second from substitute Nadir Belhadj's pass.
It was much harder work than it appeared, especially when Jermain Defoe caught centre-back Gregory in possession in only the second minute.
It looked as though Portsmouth might grab the early goal to put the tie to bed but the England striker failed to find the run of Crouch with his pass.
Guimaraes wanted a penalty in their first real attack when the ball reared up near Sylvain Distin's arm but the appeal was wildly optimistic and ignored by Turkish referee Selcuk Dereli.
However, the visitors paid the price for a sluggish start when Douglas drilled a shot into the net beyond David James in the 19th minute, with Portsmouth having made a mess of clearing a corner after Danilo's header was deflected behind.
Distin and captain Sol Campbell both failed to cut out the ball to the Brazilian who found ample space in the area to fire it home.
Douglas was booked, presumably for over-celebrating his goal, but it was not long before the home fans had something else to cheer.
Flavio gave Pompey another scare with a long-range strike and there was a sense of the inevitable when they wiped out the visitors' advantage after 32 minutes when Joao Alves' 35-yard shot from a short free-kick fizzed past the unsighted James.
Pompey had still not produced a decent effort on goal by the time they earned a free-kick just outside the area in the 40th minute, with Flavio booked for his protests.
Goalkeeper Nilson punched away Armand Traore's delivery, rising above Crouch and Campbell in a crowded area.
Johnson briefly raised hopes, cutting in from the right to hit a left-foot drive but Nilson spread himself athletically to push the effort away for a corner.
It was no surprise when Redknapp switched from his 3-5-2 to a more adaptable 4-4-2 after the break, converting Distin to an orthodox left-back and pushing Traore forward in front of him.
It almost paid instant dividends in the 49th minute when Defoe slipped in Traore as the Frenchman came racing from the wing only for his poor first touch to dribble the ball into the grateful arms of Nilson.
Soon afterwards the goalkeeper plunged to make a clean save from Crouch's cross which was aimed at Defoe.
Defoe was offside when he shot into the side-netting - but at least Pompey were finally looking a threat as the game moved towards the hour mark.
They started to dominate possession, England right-back Johnson finding plenty of scope as a right-winger.
But James had to make a save after 62 minutes when Douglas let fly from outside the area.
The long diagonal ball to Crouch's head looked the obvious route to the one goal that would win the tie on aggregate, but Pompey had to be careful not to turn it into a predictable habit.
Crouch lofted a header over the crossbar when he should have done better from Traore's cross in the 81st minute and Johnson also went close with a shot as Pompey dictated the closing stages.
But the vital away goal would not come and they were made to pay for their first half sloppiness by having to go into extra time before finally finishing off their opponents.
Redknapp savours safe passage
Harry Redknapp was dleighted to see his team battle back to claim a place in the group stage of the UEFA Cup. He said: ''It was a topsy-turvy game, and Vitoria (Guimaraes) were fantastic in the first half with their movement and passing.''We played with wing-backs again after the good result it got us at Everton,
but we didn't get the ball wide enough to make use of it until the second half.''Technically Vitoria are a brilliant side, and we couldn't cope with them
before half-time. But we changed it a bit in the second half - and after that,
there was always going to be only one winner.''You could say we made hard work of it, but we got there in the end - and
Peter Crouch took his goals very well.''The league is still our priority. But it's good to have got through to the
group stage, and we'll take it match by match from now on.''The Pompey boys had to take a dip in the sea post match to
get rid of the acid in their bodies in time for Sunday's Premier League
match against Stoke.Redknapp said: ''We have put our flight back a few hours so that the players
can get all this out of their system.''They need to get rid of the lactic acid in time for the weekend, because now
games will come thick and fast.''
Guimaraes 2 - 2 Portsmouth
