Web-borne malware continues to be a major threat on the Web. At the core of malware infection are for-crime toolkits that exploit vulnerabilities in browsers and their extensions. When a victim host gets infected, the infection dynamics is often buried in benign traffic, which makes the task of inferring malicious behavior a non-trivial exercise. In this paper, we leverage web conversation graph analytics to tap into the rich dynamics of the interaction between a victim and malicious host(s) without the need for analyzing exploit payload. Based on insights derived from infection graph analytics, we formulate the malware detection challenge as a graph-analytics based learning problem. The key insight of our approach is the payload-agnostic abstraction and comprehensive analytics of malware infection dynamics pre-, during-, and post- infection. Our technique leverages 3 years of infection intelligence spanning 9 popular exploit kit families. Our approach is implemented in a tool called DYNAMINER and evaluated on infection and benign HTTP traffic. DYNAMINER achieves a 97.3% true positive rate with false positive rate of 1.5%. Our forensic and live case studies suggest the effectiveness of comprehensive graph abstraction malware infection. In some instances, DYNAMINER detected unknown malware 11 days earlier than existing AV engines.