Sligo pulled off the result of the round last week, beating former UEFA Champions League quarter-finalists Rosenborg 2-1 at Lerkendal Stadion - a result that cost Rosenborg boss Per Joar Hansen his job.
Alan Keane and Danny North put the Irish side two away goals to the good, though goalkeeper Gary Rogers' late own-goal means they will have to focus at The Showgrounds, something manager John Coleman is aware of.
"It's only half a job and I've hammered that home to the players," he said after the game.
"We're disappointed that we conceded a goal and disappointed that we didn't take a couple of chances after that, but they're a good side and we're certainly not going to be underestimating them."
Completing a theme of Irish success were Linfield, who travel to Sweden after a 1-0 win over AIK.
Inter, meanwhile, emerged 1-0 victors against Svenska Cupen holders Elfsborg last week and will have confidence in progressing, having lost just one of their last 16 games at home - keeping clean sheets in four of their last six.
Those drawn with the bigger names to come in the third round will be hoping for a glamour tie.
Brommapojkarna look nailed on to meet Serie A club Torino as they hold a 4-0 lead over Crusaders, while Trencin can also think about a clash with English FA Cup finalists Hull City after beating Vojvodina by the same scoreline last week.
Botev Plovdiv and Mlada Boleslav will be hoping to seal meetings with PSV and Lyon after 2-1 first-leg wins over Siroki Brijeg and St Polten respectively.
Real Sociedad await the winner between Aberdeen and Groningen, with Mainz eyeing RoPs and Asteras Tripolis' clash in Greece - both games poised after draws.
Astana, Zorya, Dinamo Minsk, IFK Gothenburg, Krasnodar, Molde and Grodig are others who can look ahead after dominant first-leg victories - all hold at least a three-goal advantage.
CSKA Sofia and Motherwell will hope conceding away goals in first-leg draws does not cost them against supposedly beatable opposition in the shape of Zimbru and Stjarnan.
Other highly ranked outfits Cluj, Tromso and Bursaspor were unable to break down weaker opposition and will look to assert their dominance over Jagodina, Vikingur and Chikura after 0-0 draws.
Esbjerg and Slovan Liberec both reached the knockout rounds of last year's competition. The Danes drew 1-1 with Kairat in Kazakhstan last week, but Slovan return home after beating Kosice 1-0 away.
Omonia Nicosia, Petrolul Ploiesti, Diosgyor and Hajduk Split hold two-goal leads heading into their second legs, but things are tighter for Ruch Chorzow, Zulte-Waregem and Split who are all ahead but conceded away goals to Vaduz, Zawisza Bydgoszcz and Hapoel Be'er Sheva.
Koper, Shakhtyor and Haugesund will look to back-up narrow away wins, while Nomme Kajlu and Rijeka head to Lech Poznan and Ferenvaros protecting 1-0 leads.
Atlantas host Shakhter Karagandy, Zestafoni welcome Spartak Trnava and Metalurg Skopje go to Zeljeznicar after goalless first legs, but St Johnstone and FH will hope an away goal can swing things in their favour after 1-1 first-legs at Luzern and Neman Grodno.
