Verstappen clashed with cars twice, first with Hamilton then spectacularly with polesitter Sebastian Vettel, the two spinning at the hairpin after Verstappen ran into the side of the championship leader.
Bottas finished second and Kimi Raikkonen of Ferrari was third.
Red Bull could still be in the market to renew the Australian's deal but he remains relaxed about a likely increase in demand for his services.
By now Ricciardo was right on the tail of Bottas and was using his fresher tyres to close the gap to the lead.
Hamilton apologised to his team for losing places.
Verstappen tried passing Hamilton but ended up going off the track, he lost a place to Ricciardo in that move. Vettel maintains eighth place just in front of Sainz.
In the opening stages of the race, Vettel seemed to comfortably control the pace, keeping Bottas about 2.5 seconds behind.
The introduction of the safety auto proved a pivotal moment after marshals sought to clear debris from the hairpin after a collision between Toro Rosso's Pierre Gasly and Brendon Harley.
Daniel Ricciardo was pretty pleased with his overtaking exploits en route to victory in Sunday's Chinese GP in Shanghai. With nothing to lose, Red Bull's pit-wall crew immediately called in their drivers Max Verstappen and Ricciardo in to change their tyres from the harder medium compound Pirellis to the soft compound tyres. However, the race was all about Ferrari's poor strategy to start with and Red Bull taking advantage of the safety auto to ensure they had the fastest vehicle in the final stages of the race.
Ricciardo quickly succeeded where his teammate had failed, coming from a long way back to dive past Hamilton into Turn 14.
"Sometimes you have just got to lick the stamp and send it", he said of the move on Hamilton.
However, sterling work by his crew meant the popular Aussie headed out with under five minutes to spare, and though restricted to one flying lap in Q1 he was eventually able to put his Red Bull sixth on the grid.
After a mid-race safety auto due to the debris left on the track after Toro Rosso's Pierre Gasly and Brendon Hartley collided, Red Bull managed to make a quick decision and pitted both Ricciardo and Max Verstappen for the soft tyre to make a charge towards the end of the race.
Red Bull went into the season hoping to fight Mercedes and Ferrari for the title and a lack of reliability could prove costly with each driver limited to just three power units and only two energy stores. Alonso forced his way past Vettel on the penultimate lap of the race, even making contact with the German who had to take some evasive action to avoid even more damage.
Lap 11/56 - Brendon Hartley is the first on in the box, switching out his supersoft tires.
The battle for second went to the very end as Bottas and Raikkonen went wheel-to-wheel in the final few laps, only for the Mercedes driver to finish seven-tenths of a second clear for P2. Lewis Hamilton dropped back to fifth, as the first portion of the race passed without much incident.
Bottas held off a late surge from Ferrari's Raikkonen to finish second, albeit nine seconds down on a jubilant Ricciardo.