Kevin Thomson continues to grow in stature at Rangers and he does the simple things well.
Kenny Miller scored the only goal of the match after Kevin Thomson and Danny Wilson had been dismissed.
Kevin Thomson saw red after being penalised for a late lunge on Steven Thomson during another St Mirren advance.
Boro lost midfielder Kevin Thomson to injury, so he was replaced by Nicky Bailey, but it was still Swansea who dominated proceedings.
Hibernian's finances also made impressive reading, due in part to the sales of Kevin Thomson and Scott Brown to Rangers and Celtic respectively.
Rangers went a goal ahead when Kevin Thomson surged into the Kaunas box to get on the end of a clever pass from Nacho Novo.
Kevin Thomson was sent off for a dangerous tackle on his namesake Steven and Danny Wilson saw red for a professional foul on Craig Dargo.
It was a decent chance but Kevin Thomson's effort failed to make it past a wall of white jerseys after a tense build-up to the shot.
Kevin Thomson put Rangers ahead in the 33rd minute when he collected a Nacho Novo pass inside the box and fired past Kaunas goalkeeper Marian Kello.
Kevin Thomson returned from injury to make his European debut for Rangers and Chris Burke was given the task of supplying ammunition for Novo and Kris Boyd.
BBC: SPORT | Football | Europe | Rangers 4-0 Hapoel (agg 5-2)
The frustration of the home side threatened to boil over as Boyd was booked for leading with an elbow and Kevin Thomson saw yellow for a late lunge.
Minutes Kevin Thomson capitalised on a loose pass by Falkirk debutant Lee Bullen before driving at the defence and releasing a shot which goalkeeper Robert Olejnik held well.
Rangers responded within two minutes as Kevin Thomson's free-kick into the area eventually fell to McCulloch, who found the net with the aid of a deflection off Chris Innes.
Meanwhile, Liverpool have had a bid rejected for teenager Danny Wilson, while fellow central defender Madjid Bougherra and midfielder Kevin Thomson have all been linked with moves away from Ibrox.
Mendes became the third Rangers player to be sent off this season, following defender Madjid Bougherra in the midweek Champions League draw with Stuttgart and midfielder Kevin Thomson against Hearts on August 23.
The Scottish Premier League leaders, minus Kevin Thomson after a last-minute appeal against a suspension was turned down by the Scottish FA, looked increasingly disjointed after the break and struggled to put pressure on the home goal.
The only negative of Rangers' night in Lisbon was the bookings of captain Barry Ferguson and fellow midfielder Kevin Thomson, who will be suspended for the first leg of the semi-final against Fiorentina at Ibrox on 24 April.
Kevin Thomson, who had started the game ahead of the unfortunate Maurice Edu considering the American's solid form, whipped in a corner that was powered home by the head of the unmarked Northern Ireland international at the near post.
Alan Maybury and Kevin Moon dropped to the bench while David Robertson missed out with concussion and Pars fFull-back Jason Thomson returned from a groin injury.
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