Both sides arrived at Ewood Park on the back of differing results at the weekend.
Mark Hughes made three changes to the side that lost 2-1 at West Ham, while Christian Gross' side were still brimming with confidence following a 2-1 victory over Axpo Super League leaders and rivals Grasshoppers Zurich.
In temperatures more accustomed to the Swiss Alps, both sides made a lively start to the game.
Morten Gamst Pedersen fired a free-kick comfortably into the arms of goalkeeper Franco Costanzo on eight minutes, before the prolific Mladen Petric out-jumped Michael Gray to head narrowly wide.
And the Croatian's aerial ability was evident once again less than ten minutes later.
Brazilian Eduardo supplied the cross from the right, Petric rose unmarked in the centre, but his powerful downward header was brilliantly saved by the outstretched leg of Brad Friedel.
Basel's leading scorer this season then glanced Eduardo's pull back inches wide, before the home side found their rhythm.
After the move of the match, which included over 20 intricate passes, Shabani Nonda played in David Bentley on the right, but the England Under-21 international fired narrowly over the bar.
Rovers' goal hero from Poland last time out then turned provider on the stroke of half-time, pulling the ball back to Pedersen, but the Norwegian volleyed straight into the arms of Costanzo.
Rovers continued where they left off after the break as Nonda could have grabbed a hat-trick in the opening nine minutes from two unmarked headers and a right-foot shot.
Friedel, on his 100th consecutive appearance for the club, was still being kept busy at the other end.
He denied substitute Cristiano with a fine one-handed save, before punching clear Petric's ambitious 35-yard free-kick only for fellow substitute Delron Buckley to head wide on the rebound.
And the visitors were to rue those missed chances as Rovers broke the deadlock with a goal worthy of winning any European encounter.
On 75 minutes the ball dropped to Tugay midway inside the Basel half and after controlling it on his chest and spinning round his marker, the midfield maestro unleashed an unstoppable 30-yard screamer that flew into the top corner of Costanzo's goal.
With two minutes remaining, Pedersen was felled by Reto Zanni in the box and Jeffers scored his first goal for the club from the spot, before McCarthy netted his third of the competition in time added on to maintain Rovers' 100 per cent start to the group phase.