Bucknell (3-1) was trailing 28-24 in the first half when it went on a 10-0 run that included eight free throws and it never surrendered the lead. Thomas scored 10 of his points in the half that ended with the Bison ahead 43-36 lead, helped by a 12-of-14 effort at the free-throw line.
The Jaspers (0-2) cut into a 14-point second-half deficit, getting within six points with 6:24 to go. But the Bison responded with another 10-0 run to lead 75-69 with 3:38 remaining.
Bucknell took a total of 42 free throws. Manhattan made 13 of 20.
Shane Richards scored a career-high 28 points for Manhattan.