Jackson connected on 5 of 6 from the field, including both shots from long range, and was 10 of 12 from the free throw line as Memphis (9-3) won its third straight. Goodwin was also 5 of 6 from the field, while Geron Johnson added 10 points for the Tigers.
Dylon Cormier led the Greyhounds (9-5) with 25 points, connecting on 10 of 20 shots. Erik Etherly had 15 points and nine rebounds, while Robert Olson finished with 11 points. Etherly and Olson, however, were a combined 10 of 31, including Olson missing six of his seven shots from outside the arc.
Memphis broke the game open with 11 unanswered points in the second half.
Loyola dominated the boards, outrebounding Memphis 42-29, including 23 off the offensive glass, and held a 38-28 advantage in points in the paint.
But that was offset by the Greyhounds shooting 37.9 percent (25 of 66) and committing 19 turnovers, leading to 27 Memphis points.
Memphis led 37-33 at the half despite Cormier scoring 16 points for the Greyhounds and Loyola dominating the boards 27-16.
Cormier was 7 of 14 from the field, but the Greyhounds missed six of their seven shots from outside the arc in the frame. They would end the night 2 of 12 from 3-point range.
Jackson led Memphis with 12 points, including both of his shots from long range as Memphis connected on 5 of 8 from 3-point range.
Memphis held a trio of 10-point leads in the first half, the final one coming with just over 11 minutes remaining before the break.
Loyola answered the double-digit advantage with a 10-2 run, all 10 points by Cormier. That pulled Loyola within 30-28, but the Greyhounds could not overtake the Tigers in the final minutes of the half.
Loyola did pull even shortly after halftime as Etherly began scoring inside. But despite hitting five of their first six shots in the half, the Greyhounds could not take the lead.
Memphis' advantage could have been even larger as Loyola was called for a flagrant foul and an intentional foul in the early minutes of the half. But the Tigers were only 4 of 10 from the foul line during the early stretch.
Several times before the midpoint of the second half, the Greyhounds were within one possession, but Jackson extended the Tiger lead.
Loyola trailed 53-52 after a jumper by Olson, when Memphis scored 11 unanswered points. Goodwin had seven in the stretch, with the only other points in the rally coming when Jackson hit a pair of free throws as Loyola coach Jimmy Patsos drew a technical. A dunk by D.J. Stephens to cap the run.
The Greyhounds did not threaten the rest of the way as Memphis built the lead to as many as 16.