Neira, 17, started her round over the 6,195yd classic links' par 73 lay-out at just after 7am and she woke just about everybody up with a brilliant score of five-under-par 68.
No one got near that score until, in mid-afternoon, Engstrom birdied five par-5 holes on her way to a 69. The leading Brits were in joint third place on two-under 71 - Isobel Wardle (Prestbury) and former Junior Vagliano Trophy team player Sammy Fuller (Roehampton) - alongside Raquel Olmos Ros from Spain and Tiffany Arafi (Switzerland).
Neira comes from Gijon in the north of Spain, where she is a member of a municipal course, La Llorea, and was the Spanish Under-16 champion in 2015. She was also runner-up in this year's Anniki Invitational Europe. Paula is No. 16 in the Spanish women's rankings and 403rd in the world.
Twelve months ago she was the last of the 64 qualifier for the match-play stages at West Kilbride and then lost in the first round to the top seed from Sweden, Frida Kinhult.
But teenage girl golfers can improve tremendously over a season and Neira looked in very good nick as she had an eagle 3 at the long 12th and birdies at the par-5 seventh, 13th and 15th as well as the par-3 11th. She had only one bogey, at the 17th, in halves of 36 and 32.
Engstrom, No 23 in this week's updated Women's World Rankings, was quite happy with her 69 - and so she should be!
"It was a pretty stable round," said the blonde Swede from Ringenas Golf Club near Halmstadt where she has a handicap of +4.7.
"It could have been better. I took three to get down from the edge of the green to bogey the second and I missed a 6ft eagle putt at the seventh but, all in all, I am quite happy to score a 69."
Isobel Wardle also had gains at par-5 holes: the seventh, 13th and 15th in halves of 37 and 34. Her only bogey came early - at the first.
Sammy Fuller had as many birdies as anyone in the field of 144. She had birdies at the seventh, eighth, ninth, 12th, 13th and 15th in halves of 35 and 36 but she also bogeyed the sixth, 11th, 16th and 18th.
Raquel Olmos Ros had halves of 36 and 35 for her 71. Highlight of her card was an eagle 3 at the par-5 15th. She birdied the fifth, seventh, short ninth, and long 12th.