The 24-year-old finished ahead of the main field in the Rio velodrome but could do nothing to prevent Tatsiana Sharakova (Blr) taking victory after she gained a lap on the field.
Sharakova had attacked with around 12 laps remaining with another rider but quickly found herself riding solo and managed to make the bridge across to the main field as the no-one attempted to pick the chase up in earnest.
The riders then looked settled to take one a bunch sprint for second place, with Trott moving to the front of the pack early on with almost two laps remaining and managing to hold off Julien D'Hoore (Bel) and Sarah Hammer (USA) behind to take the place.
A small crash in the penultimate bend saw two riders go down, including Allison Beveridge (Can), but both appeared to be able to get up and finish the race with few injuries.
It means world champion Trott sits two points behind Sharakova in the overall standings on 38, with two more events in the individual pursuit and the elimination race set to take place in the second session on Monday.
Olympic Games 2016, Women's Omnium: Scratch Race
1. Tatsiana Sharakova (Blr)
2. Laura Trott (GBr)
3. Julien D'Hoore (Bel)
4. Sarah Hammer (USA)
5. Lauren Ellis (NZl)
6. Annette Edmondson (Aus)
7. Amalie Dideriksen (Den)
8. Laurie Berthon (Fra)
9. Kirsten Wild (Ned)
10. Daria Pikulik (Pol)
Overall standings after round one
1. Tatsiana Sharakova (Blr) 40 points
2. Laura Trott (GBr) 38
3. Julien D'Hoore (Bel) 36
4. Sarah Hammer (USA) 34
5. Lauren Ellis (NZl) 32
6. Annette Edmondson (Aus) 30
7. Amalie Dideriksen (Den) 28
8. Laurie Berthon (Fra) 26
9. Kirsten Wild (Ned) 24
10. Daria Pikulik (Pol) 22
Thank you for reading 20 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1