Crowdsourcing can be modeled as a principal-agent problem in which the principal (crowdsourcer) desires to solicit a maximal contribution from a group of agents (participants) while agents are only motivated to act according to their own respective advantages. To reconcile this tension, we propose an all-pay auction approach to incentivize agents to act in the principal's interest, i.e., maximizing profit, while allowing agents to reap strictly positive utility. Our rationale for advocating all-pay auctions is based on two merits that we identify, namely all-pay auctions (i) compress the common, two-stage "bid-contribute" crowdsourcing process into a single "bid-cum-contribute" stage, and (ii) eliminate the risk of task nonfulfillment. In our proposed approach, we enhance all-pay auctions with two additional features: an adaptive prize and a general crowdsourcing environment. The prize or reward adapts itself as per a function of the unknown winning agent's contribution, and the environment or setting generally accommodates incomplete and asymmetric information, risk-averse (and risk-neutral) agents, and a stochastic (and deterministic) population. We analytically derive this all-pay auction-based mechanism and extensively evaluate it in comparison to classic and optimized mechanisms. The results demonstrate that our proposed approach remarkably outperforms its counterparts in terms of the principal's profit, agent's utility, and social welfare.