Reina bundled the ball comically into his own net in the 90th minute to gift Arsenal a point, after David Ngog gave Liverpool the lead in the first minute of the second half.
Cole's Premier League debut for Liverpool went horribly wrong when he was shown a straight red card in first-half stoppage time, after launching himself unnecessarily at Laurent Koscielny close to the corner flag.
He missed the ball by a mile and scissored the Frenchman's standing leg. Malicious or not, it was a desperately bad tackle and he could have little complaint when Martin Atkinson showed the red card.
Koscielny was stretchered off, sparking fears of another long-term Arsenal injury, but the defender made a quick recovery and returned for the second half - and he was also sent off for two yellow cards, both picked up in second-half injury time.
Arsenal were no saints, particularly Jack Wilshere who started four days after making his England debut. The 18-year-old was booked for a late front-on challenge on Javier Mascherano, and might have received his marching orders had he made more contact with the Argentine.
The fouls were the major talking points of a game that took some time to get going. World Cup finalists Fernando Torres and Robin van Persie were on the bench, while Cesc Fabregas was not even in the squad.
Roy Hodgson trusted Ngog to lead the line on his own, and the 21-year-old had looked entirely unthreatening until presented with his chance just a minute after the break.
Mascherano slid a simple ball down the right channel, Ngog got half a yard in front of Vermaelen and lashed a powerful shot into the top right corner.
It was a decent shot, but Manuel Almunia should not have been beaten from that angle. Yet more evidence that the Spaniard continues to undermine Arsenal's hopes of silverware. The sooner Mark Schwarzer arrives at the Emirates from Fulham the better for the Gunners.
Despite their numerical inferiority, Liverpool continued to dominate after going in front. Martin Skrtel headed a Steven Gerrard free-kick over when well-placed, while Ngog also missed a header.
Arsenal sorely lacked their usual zip in midfield, and the second-half introductions of Theo Walcott, Tomas Rosicky and Robin van Persie made little difference.
Arsene Wenger needs captain Fabregas back to give structure, speed and imagination to a side that simply ran out of ideas in the final third.
The visitors eventually caused a few scares late on as Rosicky brought a fine save from Reina after exchanging passes neatly with Van Persie.
But it took an epic clanger from Reina to give Arsenal their equaliser. The Spaniard misjudged a cross, allowing Marouane Chamakh to bundle the ball against the post.
It bounced back to apparent safety, but as Reina attempted to collect the ball he could only scoop it into his own net. An uncharacteristic and costly error.
A frantic final few minutes saw Gerrard go close with a free-kick, while Koscielny saw red for a high challenge on Dirk Kuyt and a handball. Tremendous entertainment to finish, but on this form neither side will be genuine title contenders.