Though they were a little disunited and a minority, so was the CCP in China when they attempted to gain support - I understand that in China they had time in Yanan to consolidate their power base, but the White Guard had foreign forces to help. Why didn't they win?
The most obvious answer is that the Reds were stronger (or at least 'less weak') than their opponents but that's not particularly helpful. Instead let's look at a few areas where the Bolsheviks had a real advantage over their foes.
This was obviously beset by crises and entailed severe costs (material and political) but dwarfed the corresponding White efforts. None of the major White territories managed to put in place robust state institutions or effective local administrations. The Red state might have been chaotic but it was still more competent than the notoriously corrupt and disorganised regimes of Kolchak or Denikin.
Geography. The disorganised nature of the Whites wasn't helped by the fact that the Bolsheviks held the Russian heartlands. While the White lands weren't poor, they were too distant from each other to allow for effective coordination. That said, the flip-side to this is that the Bolsheviks were surrounded on all sides and had no real 'rear area' to rely on.
Social appeal. The biggest single advantage, IMO, that the Bolsheviks possessed is that they were fighting for Soviet power. The Bolsheviks themselves weren't necessarily the most popular but they headed a Red coalition that stood unambiguously for preserving the gains of 1917 - most notably land to the peasants, power to the soviets and a republic. This was a fragile coalition but every time it looked like fracturing then renewed White pressure would rally its factions to its defence. Even the peasantry, who were at best ambivalent about the new regime, tended to prefer it to the possibility of a restoration of the landlords.
Contrast to the Whites, who were often militarily superior. The politics of Denikin in particular were unrepentantly conservative and nationalist - he had no time for either the Bolsheviks or the Constituent Assembly and rejected land reform out of hand. There was nothing in this to appeal to the peasantry or national minorities... but then Denikin himself, thinking in purely military terms, had no interest in building a civil support base. His successor, Wrangel, recognised this and made some political gestures but this was too little, too late.
The result of all the above was that the Whites struggled whenever they emerged from their core territories. Their failure to make any concessions to the popular nature of 1917 meant that they couldn't mobilise or rely on the hostile populations that they came to govern. In contrast, the Bolsheviks could promise a better future and were pragmatic/flexible enough to mobilise and (just about) hold the Red coalition together until the war's end. Foreign aid was not enough to surmount these White weaknesses.
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