Fanendo Adi scored twice, including a goal that came in the 90th minute and appeared to give the Timbers the win at home until Gordon's equalizer off a header.
Gyasi Zardes scored in the 65th minute to even it at 1 for the Galaxy.
It was Portland's second straight draw at home to start the season. The Timbers played to a scoreless tie last weekend with Real Salt Lake.
Portland saw the return of Diego Chara, who missed the opener because of a calf contusion sustained in the preseason.
But Portland's start this season has been marked by injuries. Captain Will Johnson broke his leg last season but should return in the next three or four games. Diego Valeri, who led the team last season with 11 goals and 14 assists, tore an ACL in the final match and remained sidelined following surgery.
Midfielder Ben Zemanski had surgery to repair a ruptured anterior cruciate ligament in his right knee on Monday. He is expected to miss at least five months.
A.J. DeLaGarza was listed a reserve for the Galaxy as he continues to deal with a leg injury that limited him to seven minutes in the opener.
Goalkeeper Jamie Penedo was a late scratch. He was reportedly held out of the opener last weekend because of nagging injuries.
Fanendo Adi scored in the 31st minute, taking a pass from Rodney Wallace off a back-heel flick from Darlington Nagbe. On the run, Adi curved a blast past Galaxy goalkeeper Brain Rowe, making his second start in goal.
The Timbers had a close call in the 52nd minute, when Gyasi Zardes picked a long ball that he shot over the bar. But Zardes would find success in the 65th minute off a cross from Jose Villareal that Portland goalkeeper Adam Larsen Kwarasey couldn't stop.
Villareal has been filling the wide midfielder role that has been held in the past by Landon Donovan, who retired after last season.
Even Kwarasey joined in on the celebration of Adi's second goal, but it was short-lived.
Robbie Keane, the league's reigning MVP, was fined in the first week because of unprofessional conduct in the Galaxy's 2-0 season-opening victory at home over the Chicago Fire. Keane made a gesture following his goal with 10 minutes to play.
The match was accompanied by wild weather in Portland, marked by damaging winds and sheets or rain, along with a few bursts of sunshine.