The Swiss Super League outfit sit bottom of Group B with three points from three matches, but goal difference is all that separates them from second-placed Ludogorets.
With pool matches against Real Madrid and Liverpool to come, Basel's progression could hinge on Tuesday's result.
Basel will be in good spirits after climbing to the top of the league table with a 2-0 win over Grasshoppers on Saturday.
That result - coupled with FC Zurich's home defeat to Luzern - saw Paulo Sousa's side move first - a nice boost ahead of an important clash.
Shkelzen Gashi and Derlis Gonzalez scored the goals for Basel in a result that delighted the coach.
"After a not so good start, we were always stronger during the game," Sousa told the club's official website.
"Especially with the second half - I am very satisfied.
"I'm glad we were able to [end] this negative run [against Grasshoppers], but almost even happier about the strong performance of my team."
Basel lost to Ludogorets 1-0 last time out in the Champions League - Yordan Minev netting the 91st-minute winner.
Sousa's men have lost both of their away matches in Group A, but did beat Liverpool 1-0 in their sole home clash.
They have won six of their last nine home clashes in UEFA competition, but will be without Ivan Ivanov (knee), Marco Streller (back) and Geoffroy Serey Die (suspension).
Marcelo Diaz is free to return from a ban, though, incurred in last season's Europa League quarter-final second leg against Valencia.
Ludogorets' win over Basel - which followed plucky defeats to Liverpool and Real Madrid - was the first by any Bulgarian side in the group stages of Europe's premier club competition.
They are unbeaten in five and warmed up for their trip to Switzerland with a 4-0 league victory against Marek Dupnitsa.
Dani Abalo scored twice in that success, while Marcelinho and Roman Bezjak were also on the scoresheet.
Last term, Ludogorets won four away matches in a row in the Europa League - against PSV, Chornomorets Odesa, Dinamo Zagreb and Lazio - but they have failed to triumph in any of their last five continental road trips.
They will be keen on exacting revenge on a Basel side who knocked them out of the Champions League play-offs last term, when they lost 6-2 on aggregate.
Ludogorets will be without Minev for this match after he picked up a one-match suspension for a third yellow card of the campaign on match day three.
