Peter's attempts to Westernize Russia were successful in general because his efforts were aimed at modernizing the country. Much of this inspiration came from Peter's journeys through Europe and this included the "Grand Embassy": all in attempts to learn from European cultures and to establish alliances. To do so, Peter became more and more determined in breaking from tradition. And this involved everything from forbidding the traditional wearing of beards in "polite society" to modernizing the military to engaging with other European leaders: not just to learn from other cultures but to end Russia's isolationist policies and engage with the modern world.
Peter instituted a standing army formed by conscription (draft) and since service to the state was already a practice, it was relatively easier than in other European countries. And, the theme of service to the state was a strengthening of Peter's policies.
Peter also moved towards a more secular state. In Russia: People and Empire, Geoffrey Hosking writes:
In his concept, the state stood above selfish or partial interests, above ethnic or religious distinctions, above even the person of the monarch himself. (82)
Peter was the first Russian monarch to attempt to draw a distinction between the state on the one hand and the person and property of the ruler on the other. (82)
Peter even considered changing the royal succession (which traditionally was parent to child) to having the monarch nominate his/her successor. His general aim was to focus on the success of the state; therefore, if anything got in the way of that (the Orthodox traditions, land laws, isolationism), he would do away with it.
There was certainly resistance to Peter's reforms, not to mention the determination and often ruthless lengths he went to impose them. However, Hosking also writes:
In spite of the radicalism of Peter the Great's reforms and the widespread opposition to them in the church and among the common people, there was never any serious question of going back on them . . . (95)
Fundamentally, that was because they proved successful at promoting Russia's great power status, by making it possible to raise, equip and finance an army and navy. (95)