The Hoops began the second-leg encounter eager to go for the jugular early on, having scraped a 1-1 draw in the opening encounter at Marijampole's ARVI Football Arena.
Indeed, Celtic saw a lot of the ball in the early stages and weighed in with an early opportunity, Scott Sinclair blazing a rising shot over the crossbar after just three minutes.
Suduva, in contrast, set out to defend, with five across the back and a busy unit of three just ahead, in a bid to repel what was likely to be an offensive Bhoys display.
The Lithuanians' resistance did not hold out for long, however, Celtic drawing first blood on 27 minutes through Leigh Griffiths.
The 28-year-old marked his 100th Celtic goal in style, curling a sumptuous free kick around the opposition wall and into the back of the net from 25 yards out.
Despite their continued pressure, the Hoops could not add to their tally come the break but did not wait long after the restart to double their advantage.
In the 53rd minute, Griffiths held the ball up and set up Sinclair, who in turn found Callum McGregor inside the box, and the young midfielder calmly stroked the ball low into the corner of the net.
The tie was as good as settled just after the hour mark as Kristoffer Ajer claimed his first Celtic goal on 61 minutes, leaping in the air to bury Griffiths's deep cross into the far post.
In the end, it proved a comfortable win for Celtic, who join Old Firm rivals Rangers in Friday's group stage draw.
CELTIC (4-3-3): Gordon; Lustig, Boyata, Ajer, Tierney (Izaguirre 69'); McGregor, Brown, Ntcham; Johnston (Hayes 79'), Griffiths (Christie 65'), Sinclair
SUDUVA (5-3-2): Kardum; Svrljuga, Hayduchyk, Jankauskas, Zivanovic, Slavickas; Acevedo, Cadjenovic (Leimonas 56'), Offenbacher (Verbickas 80'); Cicilia, Gotal (Kasparavicius 73')