Max and Daniel handed the team a second double podium in a row with the Dutchman finishing in P2 for the second year in succession in Japan and with Daniel scoring his first podium finish with third place at Suzuka.
Max might have taken a sensational second victory in a row after almost closing to within DRS range of leader Lewis Hamilton in the final laps but traffic denied the Dutchman an opportunity to attack and he had to settle for second place by the championship-leading Briton.
At the start Max made a great getaway from fourth place on the grid to pull alongside Daniel as they headed towards to Turn 1. With the inside line his, Daniel was forced to back out of a challenge and Max took the place to sit third behind pole position man Hamilton and second-placed Sebastian Vettel. Forced to take an outside line through Turn 1, Daniel was then at the mercy of a hard-charging Esteban Ocon of Force India and the Aussie quickly found himself in fifth place.
Ahead, Max was on the attack again, and at the hairpin he dived down the inside of Vettel's Ferrari to steal second place.
It was clear, however, that all was not right with Vettel's Ferrari and the German was visibly struggling for pace. At the end of the following lap Ocon and Daniel closed up and easily passed Vettel, under DRS on the pit straight. Mercedes' Valtteri Bottas also powered past the Ferrari.
There followed a brief safety car period as Renault-bound Carlos Sainz's career at Toro Rosso came to an end in the gravel traps, and after being overtaken by Force India's Sergio Perez and Williams' Felipe Massa on the restart, Vettel's race engineer came on the radio to tell his driver to box and retire the car. It later emerged that a spark plug problem had been the cause of the German's early exit.
Daniel, meanwhile, was continuing to harass Ocon and eventually on lap 10 he closed on the pit straight under DRS and powered past the Force India on the left-hand side on the approach to Turn 1.
Max was the first of the frontrunners to pit, with the Red Bull driver taking on soft tyres on lap 21. Mercedes reacted and brought Hamilton in at the end of the next tour. When they both crossed the line the next time around, the undercut had narrowed the gap between the pair to just 1.8s and Max was setting purple lap times.
Daniel made his stop on lap 25. He rejoined behind Kimi Räikkönen who, like new leader Bottas, was still circulating on his starting soft tyres. Bottas, however, was running slowly on his ageing tyres and as a consequence he began to back Hamilton towards Max.
On lap 28 the deficit was just 1.1s and Hamilton was quickly on the radio to voice his concerns. A few corners later Bottas allowed the Briton to sweep past. He then dropped into the hole behind the race leader and for the next few laps he succeeded in frustrating Max and allowed Hamilton to build the gap again.
Mercedes eventually called Bottas to the pits at the end of lap 30 and the Finn emerged on supersofts, in fourth place and 10s behind Daniel. At the front Hamilton was now three seconds clear of Max and there the race for the lead stalled until the closing stage with Hamilton managing the gap and Bottas a good distance behind Daniel.
That changed in the final 10 laps of the race. Bottas now began to quickly close on Daniel and by lap 48 the Finn had shortened a 10 second gap to just 2.8s. However, Williams' Lance Stroll suffered what looked like a front-right suspension failure and the Virtual Safety Car was deployed. The enforced speed limit for the following few laps bought Daniel valuable time and when the VSC left he was able to keep Bottas at bay to claim his ninth podium finish of the year and his first at Suzuka.
Ahead, Hamilton was encountering traffic and that allowed Max to close in on the lead. However, the Dutchman was denied any opportunity to attack the Briton as McLaren's Fernando Alonso came between the leaders on the penultimate lap. The Spaniard was put under investigation for ignoring blue flags, but Max's chance had gone. He finished just 1.2s behind Hamilton to claim his second podium finish in a row, and his second consecutive P2 finish in Japan.
With Bottas fourth, fifth place went to Räikkönen in the sole remaining Ferrari. Esteban Ocon was sixth for Force India ahead of team-mate Sergio Perez, while Haas enjoyed a double points finish, with Kevin Magnussen eighth ahead of team-mate Romain Grosjean. The final point on offer went to Williams' Felipe Massa.