Celtic began the SWPL season with an impressive 3-0 win over Old Firm rivals Rangers at the K Park in East Kilbride.
New signing Nicole Pullar scored a dream debut double and Ruesha Littlejohn wrapped up the win with a fine finish.
Glasgow City got their title defence off to a strong start with a 6-0 win over Stirling University.
Hibs beat Spartans 3-0, while newly promoted Forfar began life in the top flight with a 1-0 win over Hamilton.
Celtic finished 24 points behind champions City last season, and 19 off the second Champions League spot.
Closing that gap this year is their first priority, but on this form they could give last season's top two much more trouble.
Rangers created the game's first chance - a weak effort from Carla Boyce - but after that it was a while before they got a sniff of the opposition goal.
Goalkeeper Khym Ramsay was kept busy on her debut; saving from a Kelly Clark header and a fierce Pullar shot, while Sarah Ewens also rattled a shot off the post.
However, Celtic would only be denied until the 27th minute when Rangers defended a corner poorly and Pullar stabbed the ball over the line.
Brogan Hay could have drawn the visitors level when she met a free-kick at the back post, but goalkeeper Megan Cunningham did well to save.
Four minutes into the second half, Pullar grabbed her second when the Rangers defence was slow to react at a corner, and she was given too much time to score.
By now Celtic's confidence was rising. Ewens flicked the ball to Littlejohn, who curled a delightful ball past Ramsay to make it three.
And it could have been much more but for heroics from Ramsay, who joined Rangers in midweek from Aland United in the Finnish Naisten Liiga.
Pullar was denied her hat-trick while Clark twice went close as Celtic continued to dominate.
Rangers' frustration saw Jade Gallon earn a second yellow card for a late challenge, while Lisa Swanson was fortunate not to join her in the dressing room after she appeared to kick out off the ball.
Celtic head coach David Haley: "It was a scrappy first half, but we created some great chances. The two goals we scored are probably the ugliest you're ever likely to see, but the third goal we showed a wee bit of quality.
"It was important to get a clean sheet. It's something we've spoken about for a long, long time now. I've told the girls that the biggest thing I'm pleased about today is the clean sheet.
"Nicole [Pullar] is a handful. She was brilliant, she ran the channels really well, and she scored two scrappy goals but we'll take it."
Scottish Building Society SWPL 1
Celtic 3-0 Rangers
Glasgow City 6-0 Stirling University
Hamilton Academical 0-1 Forfar Farmington
Hibernian 3-0 Spartans
Scottish Building Society SWPL 2
Edinburgh University Hutchison Vale 1-1 Hearts
Glasgow Girls 1-4 Aberdeen
St Johnstone 1-3 Central Girls Football Academy
Kilmarnock 1-2 Motherwell