With three of their batsmen on England duty, Lancashire had problems of their own before overhauling that modest target to finish on 172 for 4.
Wasim dismissed Paul Terry and John Stephenson in his first two overs and returned before lunch to trap Giles White and Kevan James in successive deliveries. After returning to remove Paul Whitaker, he polished off Shaun Udal and Heath Streak in successive balls to end the innings.
Graham Gooch's seventh century of the summer, and the 120th of his career, put Essex in command at 375 for 4 against Kent. Nasser Hussain remains unbeaten on 128.