Howley got over in the 18th minute, and fly-half Alex King converted, to put the visitors ahead by 10-6 at the break.
Two penalties from King, to go with a first-half effort, cancelled out three Jos Baxendell penalties, two in the first stanza and one in the second half, to confirm Wasps' position on the Zurich Premiership table at No.2.
Sharks, who were not able to get their attacking genius Jason Robinson into space, are still in third place.
For Sharks:Pens: Baxendell 3
For Wasps:Try: HowleyCon: KingPens: King 3