The result left the Galaxy atop Group 5 with seven points, four better than Metapan and six more than Puerto Rico. Los Angeles and Puerto Rico have one game remaining while Metapan has two. Only the group winner will advance.
The Galaxy used an entirely new starting 11 from the side that beat the Colorado Rapids 2-0 on Friday. Landon Donovan entered the game as a second-half substitute only his second match since injuring his hamstring in a friendly against Mexico in mid-August.
Puerto Rico also played without several regulars, including Osei Teleford, Hector Ramos and Josh Hansen, who came on midway through the second half to immediately add some spark to the Islanders attack.
Los Angeles had more of the possession but created few quality chances. It's best opportunity came four minutes into the second half when Kenny Walker settled a ball over the top into the area but had his poking effort pushed wide by Islanders keeper Richard Martin at the right post.
Puerto Rico came to life midway through the second half, generating four shots within four-and-a-half minutes.
Galaxy keeper Brian Perk, who has played only four games in Major League Soccer this season, went low to block Noah Delgado's right-footed effort from distance; Eddie Edward pulled a try from distance wide left; Nicolas Addlery pushed a right-footed shot just wide of the upper right corner; and Hansen volleyed a bouncer from inside the penalty into Perk.
The draw ended the Galaxy's five-game winning streak in all competitions, but extended is unbeaten run to eight.
Puerto Rico, which ended a seven-game winless slide with a 2-0 win over the Minnesota Stars, saw its three-game winning streak at home in the Champions League end.
The Islanders will host Metapan next week, while the Galaxy will complete its Group 5 schedule on October 25 against Metapan in El Salvador.