The win comes as the Government fights to reduce the high level of drug addiction in Britain and the crime associated with it.
The two agencies have been asked to develop a new campaign to raise awareness among young people of the consequences of drug abuse. The win is Mother's first since gaining a place on the COI roster in September last year.
Recent anti-drugs work focused on encouraging teenagers not to use drugs on New Year's Eve and promoting the National Drugs Helpline. Some of the most high-profile anti-drugs work came from DFGW, which won a Grand Prix at the 1998 IPA Advertising Effectiveness awards for its drugs helpline campaign.
Mother's campaign, jointly funded by the Home Office and the Department of Health working with the Department for Education and Skills, is due to break next year. It is designed to support the Government's cross-departmental anti-drugs strategy.
According to COI, the new work will target parents and carers as well as young people, raise awareness of drugs issues and guide them to sources of information. It will build on previous awareness campaigns introduced by the Government since it launched its national drugs strategy in 1998.
Jim Thornton of Mother said: "We really wanted this one. Drugs education is so important. You need both innovative thinking and a big idea if you're really going to make a difference."
Nick Bailey, the media director at PHD, added: "COI has long been a champion of an integrated approach, and we're confident that Mother and PHD's strategy will deliver this."
COI announced that it was reviewing the account in May. St Luke's had handled the brief for two years.
Mother and PHD paired up to defeat St Luke's with Manning Gottlieb OMD, Fallon with MediaVest and Delaney Lund Knox Warren & Partners with Naked.
According to a recent report by the European Monitoring Centre for Drugs and Drug Addiction, Britain has the highest level of drug use in Europe.
The survey claimed that 6.7 out of every 1,000 people aged 15 to 64 are "problem" drug users - meaning they inject drugs or have long-term cocaine, opiate or amphetamine habits.
Cocaine use by young people is also six times higher than in France and last year the number of drug-related deaths in England and Wales doubled.