Bakaev scored in the 46th and 49th minutes for Uzbekistan, before Bashar Bani Yaseen cut Jordan's deficit in the 58th at Doha's Khalifa stadium.
Uzbekistan will play either Australia or Iraq in one of Tuesday's semifinals.
Uzbekistan was in its third straight quarterfinal, while Jordan was also seeking to make it to the last four for the first time.
Bakaev, one of the five new men in Uzbekistan's starting lineup, stunned Jordan with two quick goals.
For the first, he connected with a long free kick from captain Server Djeparov behind the defense to head in unopposed from six meters out. Three minutes later, Jasur
Khasanov sent a low cross into Jordan's penalty area and Bakaev struck the ball with his left foot to beat goalkeeper Amer Shafi for the second time.
Jordan got back into the match when Bashar Bani Yaseen scored from close range. Teammate Shadi Abu-Hashhash's header from a corner was saved on the line by goalkeeper Ignatiy Nesterov, but Bashar slammed the loose ball into the net.
Nesterov and Shafi distinguished themselves in the first half, both making several good saves.
In the 23rd, Geynrikh tested Shafi with a long-range shot but the Jordan goalkeeper made a good save by tipping the ball over. On the other side, Nesterov was forced into a similar save to stop a free kick from Ahmad Abdelhalim.
Jordan midfielder Hasan Abdel-Fattah's volley beat Nesterov but went just wide of the post in the 27th minute of an open game.
Shafi made a more crucial save in the 43rd, pushing away a close-range effort from Geynrikh.
Uzbekistan's sweeping move began in midfield and the ball was moved down the right flank, with Tursunov sending over a dipping cross. Geynrikh connected with the tip of his left boot, but Shafi dived to parry the shot.
Uzbekistan lost Nesterov to an injury in the 62nd, with Temur Juraev replacing him. The team also lost influential forward Alexander Geynrikh to injury.
Uzbekistan forward Sanjar Tursunov missed an open goal with seven minutes remaining.