Chicharito scored on a penalty kick in the 65th minute and Llegtet recorded the tying goal 18 minutes later as the Galaxy (13-11-7, 46 points) stretched their unbeaten streak to four matches (2-0-2).
Jesus Ferreira and Franco Jara scored goals for FC Dallas (6-14-11, 29 points), which couldn't hold a 2-0 lead as their winless stretch reached nine (0-5-4).
The disappointing draw prevented the Galaxy from moving into sole possession of fourth place in the Western Conference.
Both teams took 12 shots. FC Dallas placed eight on target and the Galaxy put six on net.
Los Angeles goalkeeper Jonathan Bond made six saves while Dallas counterpart Jimmy Maurer had three.
The Galaxy felt the urgency in the second half and quickened their pace.
They had a solid attempt in the 53rd minute but Samuel Grandsir's left-footed shot was saved by Maurer.
Los Angeles finally got on the board in the 65th minute on Chicharito's penalty kick. He lined it up and Maurer went to his left and Chicharito booted it the other way for his 14th goal of the campaign.
The Galaxy nearly tied it three minutes later as Chicharito's header went past Maurer. But Dallas defender Matt Hedges scurried to the area and kicked the ball away before it could go into the net.
It seemed Los Angeles had knotted the score in the 75th minute when Chicharito sent a close-range shot over the sprawling Maurer. But it was overruled due to Dejan Joveljic being offside for the Galaxy.
Los Angeles kept up the pressure and did tie it up in the 83rd minute when Lletget received the cross from Grandsir and sent a right-footed shot into the net. It was Lletget's second goal of the season.
FC Dallas controlled the first half while taking the 2-0 lead.
Ferreira struck in the 30th minute after getting a drop pass from Jara. He unleashed a hard right-footer from outside the box and easily found the right corner of the net for his seventh goal of the season.
Eleven minutes later, Jara tallied to make it 2-0. Bond made the save on Ferreira's right-footed shot and Jara used his right foot to knock in the rebound for his sixth goal of the campaign.
Chicharito ties game with late goal vs. Dallas
Javier Hernandez chases down a pass and puts it in for a game-tying goal for the Galaxy vs. FC Dallas.