Republic of Ireland captain Robbie Keane put the Galaxy ahead in the seventh minute from Landon Donovan's neat back-heeled pass, only for Chris Pontius to get bottom-placed United back on level terms six minutes before half-time.
Keane turned provider in the 81st minute for Michael Stephens to notch his first goal of the season, but the hosts responded well again and secured a share of the spoils thanks to Kyle Porter's equaliser three minutes later.
Thierry Henry and Fabian Espindola were on target as the New York Red Bulls overcame Toronto FC to regain sole possession of top spot in the Eastern Conference.
Second-half goals by Chad Marshall and Dominic Oduro - both set up by Federico Higuain - overturned Marco Di Vaio's first-half opener and lifted the Columbus Crew to a 2-1 win over the Montreal Impact.
The New England Revolution twice relinquished the lead en route to a 3-2 defeat against the Chicago Fire.
Kelyn Rowe put the Revs ahead in the ninth minute and Saer Sene restored their lead in first-half stoppage time after Juan Luis Anangono had equalised. But Mike Magee got the Fire back on level terms for a second time 10 minutes after the break and Alex edged the hosts in front for the first time in the 86th minute.
Ricardo Clark headed home Brad Davis' free-kick eight minutes into the second half to hand the Houston Dynamo a 1-0 success against the Philadelphia Union at PPL Park.
The Colorado Rapids rallied for a 2-1 triumph over FC Dallas, Vicente Sanchez cancelling out David Ferreira's opener in the 59th minute before Matt Hedges' own goal midway through the second half proved decisive.
The Portland Timbers salvaged a 1-1 draw at Chivas USA courtesy of half-time substitute Diego Valeri's 50th-minute equaliser, after Bryan de la Fuente had opened the scoring midway through the first period.
Finally, the San Jose Earthquakes and the Vancouver Whitecaps played out a goalless draw.