Daniels, who spent time in the D-League this season and didn't make his pro debut until March 5, hit a 3-pointer with 11.9 seconds left to lift the Rockets a 121-116 overtime victory over the Trail Blazers on Friday night and narrow Portland's first-round playoff advantage to 2-1.
Harden finished with a career playoff-best 37 points and Dwight Howard added 24 points and 14 rebounds for the Rockets.
Aldridge had more than 40 points in each of Portland's victories in the first two games in Houston. But Asik did a good job of shutting him down in Game 3, holding the All-Star forward to 23 points. The Blazers were led by Damian Lillard with 30 points.
Portland trailed by as many as 11 points in the final quarter but Nicolas Batum hit a 3-pointer with 41 seconds left to tie the game at 110. Harden missed a half-court shot at the buzzer to send the game to overtime.
Lillard's layup gave Portland a 116-112 lead with 3:08 left in the extra period. Jeremy Lin hit a jumper from the top of the key before Harden's fadeaway tie it with 1:51 to go.
Aldridge missed a jumper over Howard but Lin missed a 3-pointer on the other end before Daniels nailed his 3-pointer.
Daniels finished with nine points in the game, all 3s.
Before the game, coach Kevin McHale told Daniels to ''be ready,'' the undrafted signee out of Virginia Commonwealth said.
''He competes,'' McHale said. ''He dives on the floor for balls. He's a tough kid.''
Batum missed a 3 with 4.9 seconds left and Harden made free throws for the final margin.
Only three teams have come back to win after losing the first two games of a seven-game series at home: The last was the 2004-05 Mavericks, who came back against the Rockets. Houston is 0-7 overall when falling behind 0-2 in the first round since the 1983-84 expansion.
Game 4 is scheduled for Sunday at the Moda Center.
''We haven't done anything yet,'' McHale said. ''We've won one game. But it feels a lot better than losing.''
The Blazers hadn't opened a playoff series 2-0 since 1977, when they got the early jump on the Lakers en route to the Western Conference title. Portland went on to beat Philadelphia for its lone NBA championship.
McHale, who acknowledged before the game that his team was frustrated, tinkered with the lineup and started Asik in place of Terrence Jones. Asik did a good job in keeping Aldridge out of the paint and the Rockets responded by coming out with intensity.
''The came out and played as they should down two games,'' Aldridge said.
Patrick Beverley's 3-pointer gave the Rockets and early 19-13 lead before Harden finished off the first quarter with a 3-pointer to put Houston up 35-24. Harden and Beverley each finished the first quarter with 11 points.
Harden was the league's top shooting guard in the regular season, but he was 14 of 47 from the field in his opening two playoff games for his worst two-game stretch of the season.
Lillard's 3-pointer tied it at 38, but Mo Williams and Robin Lopez each hit baskets to put Portland in front and cap a 16-point run. Lillard led all scorers with 16 points at the half and the Blazers had a 55-54 edge.
Harden and Chandler Parsons made consecutive 3-pointers to give the Rockets a 71-65 lead midway through the third period. But Portland - bolstered by a raucous hometown crowd - kept Houston's lead in single digits until Harden's 3-pointer made it 90-80 with 10:18 to go in the game.
Harden's jumper gave the Rockets a 100-91 lead with 6:21 left, but Lilliard made free throws that closed Portland to within 103-98 before a falling-down jumper and a foul shot to make it 103-101 with 4:05 left.
Lillard scored on a layup to put Portland in front 107-106 with 1:59 left. After Harden made four straight free throws, Batum made the 3-pointer to tie it.
''I thought we had some good looks down the stretch,Blazers coach Terry Stotts said. ''Lin Harden and Daniels made their shots. And we didn't.''
NOTES: Houston's Terrence Jones went to Portland's Jefferson High School, leading the team to three straight Class 5A championships before playing for Kentucky. ... Among the fans in the crowd for the Blazers' first home playoff game since 2011 were Sen. Ron Wyden (D-Ore.) and Detroit Lions defensive tackle Ndamukong Suh, who grew up in Portland. ... The Blazers have made at least eight 3-pointers in the in three straight postseason games for the first time in franchise history.