The twice World Cup winners finished third in the 10-team South American group, going through with Brazil, Uruguay and Colombia as the automatic qualifiers, while Peru grabbed a playoff place against Oceania champions New Zealand at the expense of Chile.
"Today Argentina took a great step forward," said coach Jorge Sampaoli. “I hope that with the time to prepare that we’ll have, we can be competitive (in Russia) like we were today.”
While Sampaoli was delighted with his captain's performance, he said the side had to stop relying on him so much.
"We've got to fix it so not everything depends on Messi," he added.
Messi had not been at his best in Argentina’s stuttering campaign and failed to score in their previous three drawn qualifiers, which had left them in sixth place and out of the qualifying berths for Russia heading into Tuesday's game.
A World Cup without Argentina seemed an even bigger possibility when Romario Ibarra put Ecuador ahead in the opening minute after he got the better of Javier Mascherano and beat Sergio Romero with a low shot.
But Argentina, who had managed only one previous win in Quito, in 2001, equalised 11 minutes later when Messi tapped home after a one-two with Angel Di Maria.
Messi then put Argentina ahead in the 20th minute, firing a superb shot past Maximo Banguera into the top corner, and completed his hat-trick just past the hour, shaking off three tired Ecuador defenders before lifting the ball over the advancing goalkeeper and into the net.
Messi, enjoying a little bit of extra space seldom afforded against rival South American defences, joined Uruguay’s Luis Suarez, his team mate at Barcelona, as the all-time joint top scorers in CONMEBOL qualifiers with 21 goals.
(Reporting by Rex Gowar; Editing by Peter Rutherford)
