After a goalless first half, the Irish minnows stunned Harry Redknapp's side when they took the lead through a close-range flick from Stephen Rice.
Rovers were ahead for 10 minutes before Roman Pavlyuchenko, Jermain Defoe and Giovani dos Santos scored in quick succession.
Juanfran's late strike saved Atletico Madrid from another dispiriting defeat as they claimed a 1-1 draw at Rennes in Group I of the Europa League.
Beaten 5-0 by Barcelona at the weekend, Atleti were on course to fall again when Victor Montano put the Ligue 1 side ahead in the 56th minute.
But Juanfran struck with three minute to play to salvage a point and ensure the 2010 UEFA Cup winners sat top of the group.
Udinese were alongside them on four points, as they left it even later to claim a 1-1 draw at Celtic.
Ki Sung-yueng put Celtic ahead from the spot in the third minute, but Almen Abdi successfully converted a penalty of his own two minutes from the end.
Ryan Donk's 90th-minute header gave Club Brugge a smash-and-grab 2-1 victory at Braga.
The Portuguese side were dominant in the first half and took the lead eight minutes after the break through Helder Barbosa, but Joseph Akpala levelled after 71 minutes before Donk's late contribution decided it.
In the other Group H game, Chris Burke and Wade Elliott scored as Birmingham came from behind to win 2-1 at Maribor, for whom Dalibor Volas opened the scoring.
Schalke's Christian Fuchs scored a goal in each half to give the German side a 3-1 win over Maccabi Haifa.
Fuchs scored in the seventh minute and again in the 65th after Idan Vered had equalised, before Jose Jurado added a third for Schalke with 10 minutes to play.
Also in Group J, AEK Larnaca picked up their first point with a 1-1 draw against 10-man Steaua Bucharest.
AEK took a 59th-minute lead through Miljan Mrdakovic before Steaua equalised through Mihai Costea, and the Cypriot side could not make the most of their man advantage following the 82nd-minute dismissal of visiting defender Pablo Brandan.
Mathias Suarez and Dieudonne Mbokani scored as Anderlecht maintained the winning start to their campaign, emerging from a battering at Lokomotiv Moscow with a 2-0 win in Group L.
Mario Haas was the injury-time hero for Sturm Graz as they found two late goals to win 2-1 against an AEK Athens side who had survived all but nine second-half minutes with 10 men.
The Greek side had taken control of their Group L match with Joachim Standfest's own-goal in the 51st minute, but Trainos Dellas was dismissed three minutes later and late strikes from Thomas Burgstaller and Haas turned the match around.
Marc Janko's double helped FC Twente heap more misery upon outclassed Poles Wisla Krakow as Co Adriaanse's men eased to a 4-1 victory in Enschede.
Wisla took a shock ninth-minute lead through David Biton, but Janko's double and goals for Luuk de Jong and Willem Janssen eased Twente home.
Andrew Johnson scored twice to give Fulham a 2-0 win at Odense in Group K's other game.
Austria Vienna inflicted more misery on hosts Malmo to get their own Group G campaign off and running with a 2-1 win.
The Swedish side had been hammered 4-1 by AZ Alkmaar on matchday one and slipped once more courtesy of first-half goals from Nacer Barazite and Alexander Grunwald.
Substitute Agon Mehmeti pulled one back for Malmo and Vienna had Emir Dilaver was dismissed late on.
Brazilian forward Taison earned Metalist Kharkiv a 1-1 draw at AZ, who had taken the lead through Jozy Altidore.
A goal 10 minutes from time by Giorgos Fotakis saw PAOK Salonika claim a 2-2 draw at Rubin Kazan in Group A.
The Greek side had taken the lead midway through the first half through Stefanos Athanasiadis, but two second-half goals by Nelson Haedo Valdez and Vladimir Dyadyun appeared to have put the Russians on course for victory before Fotakis' late intervention.
Ten-man Sporting Lisbon held on to beat Lazio 2-1 and maintain their perfect start in Group D.
Ricky van Wolfswinkel and Miroslav Klose traded first-half goals, before Emiliano Insua put the hosts back in front on the stroke of half-time with a 35-yard bullet strike. Insua was later sent off.
Admir Mehmedi salvaged a 2-2 draw for 10-man Zurich at Vaslui.
Alexandre Alphonse gave Zurich the lead, before but Zurich defender Raphael Koch was sent off for a foul on Wesley, who converted the resulting penalty in the 62nd minute.
Mike Temwanjera then put Vaslui in front in the 77th minute, Mehmedi headed the equaliser two minutes later.
First-half goals from Igor Gabilondo and Markel Susaeta gave Athletic Bilbao a 2-0 win over big-spending Paris St Germain, who had Mohamed Sissoko sent off in the 53rd minute.
Leonardo, Eulogio Zarate and Dusan Svento scored in the second half to give Salzburg a 3-0 win over Slovan Bratislava.
Goals from Peter Crouch and Jon Walters saw Stoke come from behind to claim a 2-1 win over Besiktas, who had led through Roberto Hilbert's goal.
Dor Micha struck in the 44th minute to maintain Maccabi Tel Aviv's long unbeaten record in continental competition with a 1-1 draw against Dynamo Kiev, who opened the scoring through Ideye Brown.
Goals from Luis Seijas, Felipe and Antonio Kanu saw Standard Liege beat FC Copenhagen 3-0, while Hannover won 2-1 at Vorskla with first-half goals from Mohamed Abdellaoui and Christian Pander, despite Oleksiy Kurilov's reply.
Danijel Ljuboja, Marcin Komorowski from the spot and Miroslav Radovic one minute from the end gave Legia Warsaw a 3-2 win over Hapoel Tel Aviv, for whom Toto Tamuz and Maaran Lala netted.
Wilfred Bouma, Ola Toivonen and Tim Matavz earned PSV Eindhoven a 3-1 win over Rapid Bucharest, who had opened the scoring through Dan Alexa.