It was Mexico who started the better and they might have taken the lead inside three minutes when Marco Fabian struck an effort from outside the box, but he rattled the crossbar.
Senegal responded well and so nearly levelled when Konate struck from distance, but Jose Corona pushed the ball to safety.
Senegal again came close after 21 minutes when Saliou Ciss searched out Konate in the area, but the striker just could not gather and Mexico forced the ball to safety.
Senegal continued to force chances, but Corona produced a fine save to deny a Konate header from close range.
Both sides had chances in the latter stages of the first period - with Oribe Peralta heading just wide for Mexico - but Enriquez's effort remained the only goal of the half.
Kalidou Yero so nearly levelled it for Senegal 10 minutes into the second period, but Corona palmed the ball to safety.
The pressure from Senegal continued as the hour mark approached, and Sadio Mane fired straight at Corona from close range.
It was two for Mexico after 63 minutes, however, when Javier Aquino slotted home after a mix-up in the Senegal defence.
Konate so nearly brought Senegal back into the match five minutes later when he struck a half-volley inside the box, but Corona gathered.
Konate did eventually score his fifth goal of the tournament after 69 minutes when he found the back of the net with a powerful header.
It was so nealy 2-2 moments later when Mane met a cross inside the box, but he headed just wide of the target.
However, it was indeed 2-2 after 76 minutes when Ibrahima Balde headed home from close range.
Mexico so nearly won it in stoppage time when Peralta met a Dos Santos cross, but he just headed wide as the match entered extra-time.
It was Mexico who started the extra period the stronger, and Mane kept his side in it with a series of smart saves.
Dos Santos sent Mexico into the lead after 98 minutes, however, when he stroked home after a mix-up in the Senegal defence. The African nation had chances to level before the break, but Corona kept his side ahead.
Senegal continued to push in the second period of extra-time, but Mexico added a fourth through Hector Herrera to set up a semi-final clash with Japan.