The Bhoys scored with a Henrik Larsson chip on the quarter-hour and then through Sutton’s goal in the 68th minute for a 3-0 aggregate win at Blackburn’s Ewood Park.
In other top ties, Alan Smith scored all four goals in Leeds 4-1 thrashing of Hapoel Tel Aviv in Florence, Italy, Lazio drew 1-1 at Red Star Belgrade to go through 2-1 on aggregate and Paris Saint Germain went through at the expense of National Bucharest.
Sutton, who spent five years in the north of England before finally moving across the border, got his head to a corner in the 68th minute for Celtic’s second goal to give the hosts a mountain to climb, Celtic having won the first leg 1-0 a fortnight ago.
After that occasion Celtic were given a drubbing in the English press, with Blackburn manager Graeme Souness, a Scot, saying it had been a case of “men against boys”.
However Celtic turned the tables on the former Rangers man after a performance that can only add positively to their current aim of joining the English Premiership.
As he did in the first leg, Henrik Larsson was on target scoring the opener to help him prepare his message of defiance.
In the first half Celtic were given acres of space, and defended well in all areas of the park as Blackburn struggled to find a way through.
Two weeks ago, the reverse had been the case as Blackburn ran Martin O’Neill’s side ragged all over the park in search of a vital away goal.
Celtic’s opener from Larsson gave Souness’s men a jolt. Larsson, who was given help when a Blackburn defender behind him slipped and fell, ran on to a long threaded pass from the midfield and chipped the ball calmly over the sprawling American.
Celtic’s second goal effectively killed off the match. Sutton, who is Larsson’s habitual strike partner but who had been brought back a notch into the midfield to accommodate Hartson, was parked in front of Friedel’s right-hand post.
The former Blackburn man’s flashing header beat both his marker and Friedel, who was again left sprawling.
Alan Smith made a memorable return for Leeds, scoring four goals as the English Premiership strugglers beat Hapoel Tel Aviv 4-1 for a 5-1 aggregate win.
In an often ill-tempered match at the Artemio Franchi stadium — hosted here due to the ongoing crisis in Israel — midfielder Josef Abukasis beat Leeds ‘keeper Paul Robinson with a curling shot after just two minutes.
Smith pounced on a loose ball in the penalty area after a slight deflection had turned it into his path and his shot from just left of the goal flew home on the half hour mark for the equalizer.
In the wake of Israeli pressure, Leeds scored their vital second goal of the match after a defensinve mix-up in the 54th minute.
Smith had chased down a ball on the right side of the area and while the defender waited for his ‘keeper to come out and collect, Smith stuck his foot out and poked at the ball in mid-air.
Smith added further goals in the 62nd and 83rd minutes.
Paris Saint Germain beat National Bucharest of Romania 1-0 to earn their passage.
Laurent Leroy scored in the 57th minute for a 3-0 aggregate win to put PSG into Friday’s draw in Geneva comprising 24 second round winners and the eight third-placed teams in the Champions League first round.
The round will have a real French flavour with Bordeaux winning their second round on Tuesday, and Lens, Lyon and Auxerre earning their passage by the Champions League route.
Dutch club Vitesse Arnhem drew 3-3 at German northern port city Bremen for a 5-4 aggregate win although Arnhem’s Aleksandar Rankovic of Yugoslavia had been sent off midway through the second half.
And in another surprise result, Wisla Krakow knocked out Italian club Parma following their 4-1 victory after extra time in Poland for a 5-3 aggregate win.
Thursday’s UEFA Cup second round results:
Porto 2 Austria Vienna 0
Real Betis 3 Viktoria Zizkov 0
Levski Sofia 1 Sturm Graz 0
Wisla Krakow 4 Parma 1
Blackburn Rovers 0 Celtic 2
Fulham 2 Dinamo Zagreb 1
Slavia Prague 5 Partizan Belgrade 1
Werder Bremen 3 Vitesse Arnhem 3
Grasshoppers 1 PAOK Salonika 1
Paris St Germain 1 National Bucharest 0
FC Midtjylland 0 Anderlecht 3
Panathinaikos 4 Fenerbahce 1
Slovan Liberec 1 Ipswich Town 0
Anorthosis Famagusta 0 Boavista 1
Viking Stavanger 1 Celta Vigo 1
Red Star Belgrade 1 Lazio 1
Besiktas 1 Alaves 0
Schalke 04 0 Legia Warsaw 0
Hapoel Tel Aviv 1 Leeds United 4
Denizlispor 2 Sparta Prague 0
—AFP/Reuters