Both teams raced out of the traps, and Toby Ajala came close for the visitors with the game's first chance.
Hawley spent last season at Torquay and netted against his former club in the 17th minute with a poacher's finish.
Once more, Briscoe restored parity with a simple finish from close range in the 53rd minute as the visitors refused to give in.
However, Hawley was keen to prove his quality to the side who let him leave in the summer, and, in the 70th minute the 32-year-old nodded the ball into the path of Paul Clayton, who sent a delightful chip over Martin Rice to give Alfreton the lead for the third time in the game.
With Torquay in search of an equaliser, Hawley grabbed his second of the game when he pounced on a suicidal Courtney Richards backpass to secure all three points for the Reds 12 minutes from time.