The win was the second in three days for the Minutemen, while LSU, which led only once in the game at 3-0, lost its season opener.
UMass, picked to finish fourth in the Atlantic 10, held LSU, tabbed fourth in the SEC, without a field goal for over five minutes down the stretch but almost squandered an eight-point lead in the final 63 seconds.
Williams started slowly for the second straight game but again came through after the shaky start. He had nine assists and three rebounds.
Carter finished with 17 points and Raphiael Putney added 14 points and nine rebounds for UMass (2-0).
Johnny O'Bryant, who sat out much of the second half of the foul-filled game with four personals, led LSU with 23 points, 11 rebounds and two blocked shots. Stringer had 21 points and Jordan Mickey and Anthony Hickey added 16 points apiece -- Mickey, in his freshman debut, grabbed 10 rebounds and blocked five shots.
There were 54 fouls in the game, with the officials enforcing the new hands-off NCAA rules.
Lalanne, the first A-10 player of the week after scoring a career-high 27 points, grabbing 12 rebounds and blocking three shots in Sunday's win over Boston College, picked up two fouls and played only four minutes in the first half. He then went 8-for-9 from the floor in the second half before fouling out with 2:15 remaining.
UMass, despite a field goal drought that lasted almost eight minutes, led by as many as 10 in a first half littered with 33 fouls. But LSU, which started three freshmen and a sophomore, charged back, closing the deficit to one before a Williams 3-pointer with five seconds left in the half made it 49-45 at the break.
LSU freshman Jarell Martin, playing his first college game, limped off the court just 33 seconds into the game and didn't return.
The game, the first ever between the two programs, began at 11 a.m. as part of ESPN's college basketball marathon.