LaMarcus Aldridge had 18 points and 14 rebounds, his 40th double-double, and Nicolas Batum added 15 points to keep Portland in the race to host a first-round playoff series.
Derrick Favors scored 21 points and Enes Kanter had 15 points and 13 rebounds, but the Jazz have lost eight of nine.
Early in the fourth quarter, the Jazz led by two and Lillard hadn't converted a single field goal.
Over the next 3:24, Lillard made four 3-pointers and a pair of free throws.
After that, the Blazers led by double-digits for the first time at 96-85 with 6:28 remaining and soon earned their seventh victory in their past eight games.
Marvin Williams was out with a knee bruise and the Jazz started the five players that figure to be the core as they rebuild.
The quintet -- Gordon Hayward, Favors, Kanter, Trey Burke and Alec Burks -- are all 23 years or younger and have gained experience during this often-frustrating season for a franchise that once made the playoffs 20 years in a row.
Burks has primarily filled the sixth-man role while veteran Richard Jefferson had been the only Utah player to start (and play) every game this season.
The youthful lineup paid dividends early, but the Jazz struggled down the stretch against a better team as they have all season. Burks had 16, Burke had 14 points and 11 assists and Hayward added 14, but no one could stop Lillard when he was determined to score in the final period.
The Blazers drew within a half game of Houston for the fourth slot in the Western Conference as Minnesota edged the Rockets 112-110 on Friday.
Portland won its last road game of the season and has two remaining at home. The Blazers swept the Jazz for the first time in franchise history.
The Blazers' defense had improved over the past few months but the Jazz got the shots they wanted, for the most part, until Portland clamped down in the fourth and scored 35 points on the other end.
The Blazers went 7 for 8 from beyond the arc in the final period and though they were outrebounded by a 47-41 margin, Portland grabbed four offensive rebounds to get second shots down the stretch.
The Jazz led most of the first half before Matthews scored 10 points in the final 3:09 of the second period to lift the Blazers to a 53-51 advantage at the break.
The Jazz next play at Denver Saturday night.