Adlene Guedioura was sent off after being yellow carded a second time 55 minutes into a friendly international in the Dutch capital, The Hague.
Algeria trailed, then led before conceding a second goal three minutes from the end of regular time to set up a tense finish.
Jesus Manuel Corona put the Mexicans ahead on 43 minutes in only the second match between the countries with Mexico winning a World Cup warm-up in 1985.
Ismael Bennacer levelled before half-time and Manchester City winger and Algeria captain Riyad Mahrez put his country ahead midway through the second half.
The two-time Africa Cup of Nations winners held that advantage with 10 men until Daniel Lainez equalised.
Algeria last lost in October 2018, away to Benin in a 2019 Cup of Nations qualifier, and have since won 16 competitive and friendly internationals and drawn four.
The 20 matches have been against African opposition apart from victories over Qatar and Colombia and the draw with Mexico.
Before travelling to the Netherlands, Algeria defeated Nigeria 1-0 in Austria last Friday in a repeat of a 2019 Cup of Nations semi-final won by a Mahrez free-kick thunderbolt.
Like many other African countries, Algeria used the October 5-13 FIFA international window to prepare for the resumption of 2021 Cup of Nations qualifying.
– Nigeria miss penalty –
Matchdays 3 and 4 will be played next month after a lengthy delay caused by the coronavirus pandemic, and Algeria face Zimbabwe home and away in Group H.
Meanwhile, Nigeria and Tunisia drew 1-1 in the Austrian town of Sankt Veit an der Glan in another rematch from the 2019 Cup of Nations tournament in Egypt.
Nigeria won a third-place playoff last year, and started promising in pursuit of another victory over Tunisia as Leicester City forward Kelechi Iheanacho netted on 21 minutes.
He had a chance to score again not long after, but his weakly struck penalty was saved by Farouk Ben Mustapha, whose foul on Nigeria captain Ahmed Musa led to the spot-kick.
Tunisia, who trounced Sudan four days ago, recovered to level a minute from half-time through Mohamed Drager, but there was no further scoring.
After drawing with Belgium, the number one ranked football nation, last week the Ivory Coast fell 1-0 to Japan in the Dutch city of Utrecht.
Unmarked Naomichi Ueda snatched a late Japanese winner with a diving far-post header past goalkeeper Sylvain Gbohouo.
The Ivorian line-up included former Arsenal attacker Gervinho, recalled for the first time since 2017.
Morocco failed to build on an impressive win over top ranked African team Senegal last week and could only draw 1-1 with the Democratic Republic of Congo in Rabat.
Noussair Mazraoui put the hosts ahead on the stroke of half-time, but a Congolese side severely depleted by withdrawals levelled through Yoane Wissa.
