Messi was floored by a strong tackle and some PSG players stopped playing in the build-up to Seko Fofana's goal which gave Lens a 62nd-minute lead in northern France.
It looked as if that would be enough for Lens to claim a victory which would have been just reward for an outstanding performance that delighted their supporters in a crowd of close to 37,000.
However, PSG equalised in the second minute of injury time as Kylian Mbappe crossed for fellow substitute Wijnaldum to head home.
It is a second draw in as many matches for the Qatar-owned club, who extend their lead at the top of Ligue 1 to 13 points from Marseille, beaten 2-1 at home by Brest earlier on Saturday.
Despite their big lead at the top of the table, it was yet another unsatisfactory performance from Mauricio Pochettino's disjointed team of superstars, who have usually had enough individual talent to get results this season but have rarely convinced.
Six of their league wins in this campaign have come with goals scored from the 79th minute onwards, and here they were rescued by Wijnaldum's last-gasp intervention.
It was a PSG side missing Neymar, who is out with an ankle injury and not expected to return before mid-January, while their nine-goal top scorer Mbappe was rested at kick-off before coming on to help save the day.
Messi still has just one goal from nine Ligue 1 appearances and he struggled to make his presence felt against an impressive Lens side who lie fifth in the table.