The hosts dominated possession at Celtic Park and Scott Sinclair's finish after four minutes set the tone.

Sinclair scored again after the second half opened with Tom Rogic's superb long-range strike, with Stuart Armstrong netting in stoppage time.

Celtic meet Rosenborg of Norway next, with the first leg in Glasgow.

Linfield set out to try to contain the Scottish Premiership champions, but their resistance faltered and goalkeeper Roy Carroll produced two excellent saves in keeping with his performance in the first leg last Friday in Belfast.

He denied Moussa Dembele in the first half, and then Sinclair as he looked to complete his hat-trick with a dipping shot from long range before the end.

Olivier Ntcham made his debut for Celtic following his move from Manchester City.

Celtic's two-goal advantage from the first leg at Windsor Park was always going to be added to in a substantial way, the only question being how many they would manage to get.

A vast home support turned out, and they were rewarded with a goal inside four minutes when a shot from Ntcham broke to Sinclair, who scored from a tight angle.

The sense then was an onslaught was coming, but it was an onslaught that took a long time to reap more goals.

Celtic had multiple chances but could not find the accuracy to convert them. Dembele, Rogic and Sinclair had two excellent opportunities apiece before the break but all of them went begging. At least two were sitters.