Although a pair of early Stephen Myler penalties eased Saints in front, a converted try against the run of play from Myler's opposite number, Igancio Mieres, gave the Warriors a 7-6 lead going into the break.
Myler and Chris Pennell exchanged penalties after the break, but with Worcester looking on for what would have been a shock result Saints struck with three tries in quick succession.
Samu Manoa marked his return to the club with a dive from close range, wing Tom Collins grabbed his first senior score with a good finish, and flanker Tom Wood sealed the six five minutes from time.
The end result was a touch harsh on Worcester, who battled manfully for the first hour, and Ma'afu said that the Warriors deserve praise for the way they stayed in the contest.
"They were definitely up for the game today," he told SaintsTV. "It was a matter of us building pressure and staying in the mix, keeping wearing them down and getting the result at the back end of the game.
"We knew what was coming after what we'd seen during the week, so we knew there were areas that we wanted to build pressure, and we got a good result in the end."
Mieres' try had come just before the break to stir Sixways into life, and Ma'afu said that the visitors' reaction was pleasing.
"The way we came out and reacted after half-time was a good effort from the 15 on the field," the Australian added. "And the impact that the bench had when they came on was a credit to the team."