Rangers, which beat German champion VfB Stuttgart, 2-1, two weeks ago, is tied with Barcelona for first place in Group E with a maximum six points after two matches.
Last-place Lyon had won its first-round group the last four seasons, finishing ahead of the likes of Real Madrid (twice), Manchester United and Bayern Munich.
Rangers got goals from Lee McCulloch, Frenchman Daniel Cousin and Beasley and a lot of luck in the form of three Lyon shots off the woodwork -- two by star Juninho and one by Brazilian teammate Anderson.
McCulloch scored in the 23rd minute when he headed home a Beasley corner.
Rangers made it 2-0 after 48 minutes when Cousin scored off with a powerful shot an Alan Hutton cross from the right.
Five minutes later, Beasley collected Cousin's long pass, broke through the Lyon backline and beat goalie Remy Vercourte with a cool finish.
Beasley became the first American to score in the Champions League proper with two clubs. He had four goals with PSV in 2004-05 when the Dutch club reached the semifinals.
Rangers manager Walter Smith:
"It's an excellent result. We defended very well. We have a new team and we had to see how they would be away from home. Nobody would have imagined we could net three against Lyon."
Lyon president Jean-Michel Aulas:
"From a statistical point of view, it's going to be very tough to qualify. We did not see such a defeat coming."
Oct. 2 in Lyons
Lyon 0 Rangers 3. Goals: McCulloch 23, Cousin 48, Beasley 53.
Lyon -- Vercoutre, Reveillere (Clerc, 81), Squillaci, Anderson, Grosso, Juninho, Bodmer (Ben Arfa, 60), Kallstrom, Govou, Baros (Keita, 60), Benzema.
Rangers -- McGregor, Hutton, Cuellar, Weir, Papac, Hemdani, Beasley (Adam, 90), Ferguson, Thomson, McCulloch (Novo, 80), Cousin (Whittaker, 66).
Referee: Tom Ovrebo (Norway).