The oil and gas conglomerate and Fifa, the world governing body, sign major sponsorship agreement
The Finn, who turned 31 on Friday, lapped the seven km Spa-Francorchamps track in one minute 44.493 seconds, beating Hamilton by just 0.069 seconds on a cool and cloudy morning.
Max Verstappen was best of the rest again in third for Red Bull.
The Dutchman, who has a Belgian mother and is missing the support of his army of orange-clad supporters who usually throng the grandstands at Spa, was hot on the Mercedes pair's heels, ending the session just 0.081 seconds off the pace.
Hamilton, winner of four of this season's six races and currently in the form of his life, leads the overall standings by 37 points from Verstappen.
Bottas, who won the season-opening Austrian Grand Prix in July, is third 43 points behind his team mate.
With 11 of this season's 17 races still to run, he needs to start turning the tide if he is to have any hope of denying Hamilton a record-equalling seventh title at the end of the year.
Sergio Perez was fourth in his Mercedes-inspired Racing Point ahead of Canadian team mate Lance Stroll.
Alexander Albon, who drove his first race for Red Bull at Spa last year after moving up from junior team Toro Rosso now rebranded Alpha Tauri, was sixth.
Esteban Ocon, who made his Formula One debut in Belgium in 2016, was seventh for Renault ahead of McLaren's Carlos Sainz.
Daniel Ricciardo was ninth in the other Renault with Briton Lando Norris rounding out the top-10 for McLaren.
Ferrari, winners for the last two years in Belgium, continued to struggle.
Charles Leclerc, who took his maiden Formula One win at the Spa circuit last year, was only 14th ahead of departing four-time champion Sebastian Vettel in 15th.
The session was largely uneventful.
All cars carried special stickers in memory of Frenchman Anthoine Hubert, who suffered fatal injuries in a Formula Two race on the Saturday of the Belgian Grand Prix weekend last year.
Power unit issues sidelined both Haas cars. Technical issues limited Alfa Romeo's Antonio Giovinazzi to just two laps.
Bottas suffered a late-session puncture but returned to the pits without incident.
When informed about it on the radio he quipped: "I'm getting used to these punctures, I had a puncture last weekend in my road car."
The oil and gas conglomerate and Fifa, the world governing body, sign major sponsorship agreement
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It's a treatise that would determine the course of your life, not just academically, but as a person too