Celtic will take a three-goal lead into the second leg of the Champions League second qualifying round tie with Irish Premiership champions Cliftonville.
The Scottish giants dominated the first half and were rewarded with goals from Mikael Lustig and Georgios Samaras.
The home side came into the match more after the break but James Forrest put the outcome beyond doubt with a right-foot strike late in the game.
The return leg will be played at Celtic Park next Tuesday.
Celtic went into the game hoping to emulate their progress to the last 16 of Europe's most prestigious club competition last season.
But a pre-season tour to Germany which saw them lose four games, conceding 12 goals, was not the preparation they would have wanted.
Bhoys boss Neil Lennon indicated that he was taking the threat of the Irish league part-timers seriously by naming a strong starting line-up, while his counterpart Tommy Breslin also signalled attacking intent with his formation.
Any fears the visitors may struggle to come to terms with the artificial surface were quickly dispelled as the Scottish champions bossed the opening period.
Mikael Lustig opened the scoring for Celtic at Solitude
Kris Commons saw his back-post header bounce off the woodwork after just two minutes and the attacking midfielder squandered a chance 15 minutes later when his first touch let him down following some poor Cliftonville defending.
Beram Kayal fired a right-foot shot wide and home skipper George McMullan almost mis-kicked into his own net, managing to put the ball behind for a corner.
Commons sent over the resulting corner and Swede Lustig timed his run perfectly, rising highest to head home after 25 minutes.
Liam Boyce had a sight of goal for the home side soon after, but his right-foot effort was easily gathered by Fraser Forster.
Samaras doubled Celtic's lead on 31 minutes when he turned and fired a left-foot shot past Conor Devlin.
Six minutes before the break, former Derby player Commons made room at the edge of the area, but his right-foot curling shot rebounded off the bar.
The Reds began the second half brightly and Stephen Garrett had a half-chance but was unable to make a good connection as he attempted to lob Forster.
Boyce then produced some good work on the right and found strike partner Joe Gormley, but his drive was blocked by Nigeria international Efe Ambrose.
Ciaran Caldwell went close and Barry Johnston fired over for the hosts, but as they began to tire Anthony Stokes almost added a third, hitting the bar with a left-foot shot and then whistling a long-range drive past Devlin's left-hand post.
With 10 minutes remaining, Forrest was off-target with a well-struck drive but he found his range soon after, taking on Jaimie McGovern before beating Devlin at his near post to seal the victory.
- 12 Devlin
- 02 McGovern Booked
- 03 Scannell Booked
- 07 Caldwell (Donnelly - 73' )
- 16 Smyth
- 04 Johnston
- 08 McMullan
- 17 Catney
- 10 Garrett (Curran - 78' )
- 19 Gormley (O'Carroll - 69' )
- 27 Boyce
- 01 Brown
- 15 Seydak
- 11 Donnelly
- 13 McNeill
- 20 Curran
- 23 Cosgrove
- 14 O'Carroll
- 01 Forster
- 03 Izaguirre
- 04 Ambrose
- 06 Wilson
- 23 Lustig
- 08 Brown
- 15 Commons (Rogic - 81' )
- 33 Kayal Booked
- 49 Forrest (McGeouch - 86' )
- 09 Samaras (Watt - 76' )
- 10 Stokes
- 24 Zaluska
- 59 Waters
- 18 Rogic
- 36 Irvine
- 46 McGeouch
- 17 Balde
- 32 Watt
Ref: Sergiy Boiko