The match had just moved into stoppage time when Wells was brought down just outside the penalty area by Mathieu Baudrey, which earned the Orient defender a booking and up stepped the Bermuda international to curl the ball into the top corner for his 15th goal of the season.
The visitors went in front in first-half stoppage time when Lloyd James controlled the ball from a throw-in on the left and turned smartly before beating Bradford keeper Jon McLaughlin with a superb shot into the far top corner from just outside the penalty area.
Slade was without his leading scorer, the suspended David Mooney, while his other main striker, Kevin Lisbie, was on the bench after recovering from injury.
Slade said: "We were missing 28 goals, but the two lads who took over did really well and it was a good hard-working performance.
"Lloyd James' goal was a fantastic strike and although we conceded a late goal the point we earned could turn out to be very important.
"Bradford City are very direct and ask of lot of questions of your back four, but our keeper didn't have to make a save in the second half and what pleases me is how well we played without the ball.
"We have a terrific work ethic. There is no way this group will roll over and we went to the 91st minute before we conceded a goal.
"We were disappointed with that, but maybe it was a fair result and I think Bradford are going to feel happier than we are."
Up to Orient taking the lead, Bradford had had the best chances with James Hanson and Garry Thompson heading wide and winger Kyel Reid forcing visiting keeper Jamie Jones into a superb save to keep out a fierce 20-yard shot and had at least one penalty appeal turned down.
Nathan Doyle, Wells and James Hanson all went close for them in the second half, but Orient looked set for their eighth away win of the season until Wells' last-gasp equaliser.
Despite conceding that late equaliser, Orient strengthened their position at the top of the table because second-placed Wolves, who had been level on points, lost at home to MK Dons, which gives the east London side a one-point lead.
Manager Russell Slade was without his leading scorer, the suspended David Mooney, while his other main striker, Kevin Lisbie, was on the bench after recovering from injury.