The 34-year-old ran clear and calmly slotted in with nine minutes to go to settle the encounter.
Extra time was needed after Chris Tierney's late leveller for New England had cancelled out Gyasi Zardes's goal.
The win ensured that all-time leading MLS scorer Donovan ended his career with six championship titles.
The former Everton attacker said: "I'm in a little bit of a daze, to be honest.
"I don't know. There's a lot going on. There's a lot of obvious excitement. Some sadness. There's uncertainty. And just pure joy for this team and for what we did.
"It just feels a bit strange, I guess is the best way to put it. But all in all, I'm really proud of what this team accomplished this year, and it's so nice to be in that locker room and see so many happy faces, and for me that's as enjoyable as anything now, as you get older."