Abrahams and Jackson secured Lyon's 34-20 win over Connacht Rugby on Saturday at the Matmut Stadium de Gerland.
Number 8 Sean Jansen took Lyon by surprise when he put the visitors ahead with a seventh-minute try, flying through from his own half and into the corner, but the French side hit back quickly, with tries from wing Thaakir Abrahams and full-back Alexandre Tchaptchet, both converted by Jackson.
Jackson added two penalties before the break as the hosts dominated possession, and Lyon looked likely to extend their advantage even further.
But flanker Cian Prendergast's essay down the line closed the gap three minutes before half-time, sending Connacht Rugby ten points behind.
And they took that momentum into the second half, with Connacht Rugby's power and efficiency pushing hooker Tadgh McElroy over the line, followed by JJ Hanrahan adding the extras.
It was the impetus Lyon needed to push on, though, with Number 8 Mickael Guillard's try converted by Jackson in the 52nd minute.
Hanrahan's penalty on 67 minutes made the closing stages more tense as Connacht continued to press.
But a late try from Abrahams, this time converted by replacement Léo Berdeu, extended the margin of victory and made the last four minutes much more comfortable for the hosts.
The Westerners are still without a win in the competition and sit bottom of the pool.
Meanwhile, Lyon now have two victories to add to their two losing bonus points at Bristol Bears.
Scorers:
Lyon: Tries: Thaakir Abrahams (2), Alexandre Tchaptchet, Mickael Guillard. Conversions: Paddy Jackson (3), Léo Berdeu. Penalties: Paddy Jackson (2).
Connacht: Tries: Sean Jansen, Cian Prendergast, Tadgh McElroy. Conversion: JJ Hanrahan. Penalty: JJ Hanrahan.
Teams:
Lyon: 15 Alexandre Tchaptchet, 14 Monty Ioane, 13 Josiah Maraku, 12 Thibaut Regard, 11 Thaakir Abrahams, 10 Paddy Jackson, 9 Martin Page-Relo, 8. Mickael Guillard, 7. Arno Botha (captain), 6. Liam Allen, 5. Romain Taofifenua, 4. Joel Kpoku, 3. Demba Bamba, 2. Yanis Charcosset, 1. Hamza Kaabeche. Replacements: 16 Guillaume Marchand, 17 Jérôme Rey, 18 Paulo Tafili, 19 Ugo Vignolles, 20 Maxime Gouzou, 21 Liam Rimet, 22 Léo Berdeu, 23 Alfred Parisien
Connacht: 15 JJ Hanrahan, 14 Andrew Smith, 13 Tom Farrell, 12 Tom Daly, 11 Shayne Bolton, 10 Jack Carty (captain), 9 Michael McDonald, 8 Sean Jansen, 7 Jarrad Butler, 6 Cian Prendergast, 5 Joe Joyce, 4 Darragh Murray, 3 Jack Aungier, 2 Dylan Tierney-Martin, 1 Peter Dooley. Replacements: 16 Tadgh McElroy, 17 Denis Buckley, 18 Dominic Robertson-McCoy, 19 Oisin Dowling, 20 Conor Oliver, 21 Matthew Devine, 22 David Hawkshaw, 23 Shane Jennings