I suppose it depends what one means by "underclass" (and there has even been a long tradition of debating whether November 1917 was actually a revolution or not), but I don't think even the Bolsheviks would characterize their revolution as one from the lowest rungs of society.

To condense Marxism-Leninism to an incredibly short paragraph: what Lenin saw his party doing was being a "vanguard party", ie a tightly organized group of professional revolutionaries who were leading the industrial working class in a political revolution to build socialism. The idea here is that the Bolsheviks were natural revolutionary leaders because they had the "key" of understanding Marxism, especially Marxist historic progression, and they were very well organized. The Bolsheviks themselves tended to see the industrial working class as their "core constituency", if you will - they tended to recruit among industrial workers, and were first and foremost looking out for those workers interests (at least in theory and in their public declarations).

But the industrial working class in the Russian Empire was in fact a small minority of the population. Just to put things in perspective: the entire Russian Empire population in 1913 was 170-174 million, with about 140 million-ish living in territories that would be the Soviet Union after 1922 (the rest being in places like Finland, Poland, the Baltics and Moldavia that would be not Soviet during the interwar period). Even with a steady pace of industrialization starting in the 1890s, with some big advances in areas like oil production and railroad construction, the empire was overwhelmingly rural and agricultural: something like more than 100 million peasants working holdings in villages and at least 80% of the population living in rural areas. General counts of manual wage earners will tally 15 million or so people, but even here only 2 to 3 million were industrial factory workers (the balance often working in small businesses, in construction, mining, domestic service or as day laborers). Interestingly, a lot of those industrial workers (something like 1.5 million) were employed in state-owned enterprises, especially in industries like armaments and shipbuilding. A more expansive definition of wage earners will push the total to 26 million, and that will include about 1.4 million railroad workers, but also 6.5 million wage laborers in agriculture.

Interestingly, one area that saw strong support for the Bolsheviks was in the Russian army, mobilized in the First World War. It had a much higher literacy rate than the country as a whole (something like 75% of the army was literate, compared to 30% or so nationally), and disproportionately drew on manual workers for its mobilized numbers (a third of industrial workers of all types, or about 4 million, joined the military during the war, and the total mobilized by 1915 was a little over 15 million). This mobilization did cause worker shortfalls, but a lot of this was made good through refugees and POWs over expanding the overall size of the industrial workforce per se.

So overall, these two sections of society - industrial workers and the rank and file of the Russian military - tended to show the strongest support for the Bolshevik Party in 1917 and after. They were not an elite, but at the same time they were not the poorest parts of society: they were urban, relatively highly skilled, and relatively well-educated (and overwhelmingly European and male) compared to the overall population. Furthermore, especially in parts of the empire that would break away (or try to) after 1917, Bolsheviks and socialist parties in general had to compete with nationalist parties of various ideological flavors.

The largest (and overall poorest) parts of society in the Russian Empire were the peasantry, although even they are not all one undifferentiated mass, as economic conditions could vary greatly from region to region, village to village, and family to family. But overall the peasantry and Bolsheviks tended to view each other with mistrust - the Bolsheviks had almost no presence in the countryside until basically collectivization and the First Five Year Plan starting in 1929, and even in 1917 Lenin's support of things like land-redistribution (the absolute number one priority of the peasants) was more of a tactical recognition of a fait accompli than something the Bolsheviks led the way on. In general the peasantry favored the Socialist Revolutionaries, who were a socialist party that specifically saw the peasants as their natural base of support.