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Bottas, on the fastest ultrasoft tyre compound, ended the 90 minutes with a very slim 0.035s advantage over Ricciardo - notably on the 'slower' supersoft rubber - while Lewis Hamilton, who came home fourth, was almost a second behind his Mercedes team mate. And Force India showed signs of serious improvement, with Sergio Perez and Esteban Ocon third and fifth respectively.
Williams too looked more competitive, with Sergey Sirotkin in eighth and Lance Stroll - on the podium here last year - in 11th.
Ferrari, meanwhile, had a surprisingly low-key first afternoon. Sebastian Vettel could do no better than tenth, the German complaining of poor rear grip as he failed to set a representative time, while team mate Kimi Raikkonen managed just 10 laps before being confined to the garage with a technical issue.
It was an interesting start to the session, with teams finding grip hard to come by in the early stages. Mercedes sent Hamilton and Bottas out on the supersofts, and it was the latter who set the first time of P1 before Hamilton temporarily took control.
Baku provided an enthralling race last year and it didn’t take long for the drivers to encounter the tricky Turn 8, with Toro Rosso's Brendon Hartley the first to take to the escape road - a theme that would continue throughout the session as numerous drivers ran off track in various places as they explored the limits of adhesion.
With Mercedes on the supersofts early on, there was a mixed bag of tactics on show. Ferrari opted to run the ultrasoft rubber while Red Bull gave the yellow-marked softs a run out.
It was indeed Red Bull who were beginning to stake their claim as the quickest, with Verstappen running well and, at one stage topping the timesheet, before his session ended in dramatic fashion.
The young Dutchman, who has had a string of high-profile incidents already this year, lost the rear heading into Turn 5 and despite an attempt to correct himself, his Red Bull swiped side-on into the barriers.
That signalled the end of his FP1, meaning it was down to Ricciardo to lay down the gauntlet for Red Bull and the Australian, full of confidence after his China victory, was enjoying plenty of pace in the middle sector.
The lead was swinging between Hamilton and Ricciardo before Bottas produced a stunning lap on the ultrasofts to go almost a second quicker.
Red Bull’s Chinese Grand Prix winner then reduced that deficit - a boost for them given he was on the supersofts - but there will be concerns regarding Verstappen's car.
Certainly one to keep an eye on in FP2...