Eriksson, No. 510 in the rankings, was given a wild-card slot at the tournament in his home country and made Alund work to advance. The two played for nearly 3 1/2 hours before Alund completed a 7-5, 6-7 (5-7), 7-6 (10-8) win.
Alund had one more break, which gave him the first set, but won only nine more points (158-149) over the course of the match.
He was up 6-3 in the final tiebreaker but Eriksson fought off all three match points. Eriksson got to an 8-7 lead for a match point of his own but Alund won the next three points to advance.
Alund plays top-seeded Tomas Berdych, sixth in the world, in the next round. Berdych had a first-round bye.
Other main-draw matches Monday saw Carlos Berlocq defeat seventh-seeded Horacio Zeballos 6-4, 6-3 by saving all seven break points Zeballos managed and No. 5-seeded Grigor Dimitrov edge Elias Ymer 5-7, 6-2, 6-4.