Swansea went ahead five minutes before the break when an attempt to clear by Liverpool's 75 million pounds defender Virgil Van Dijk landed at the feet of Mawson who swept the ball home for his sixth league goal this season.
Van Dijk, playing in his first league game since signing from Southampton, had earlier flashed over a header from a first-half corner, while Mohamed Salah blazed the Dutch defender's lofted pass over the bar on the half-hour mark.
