The visitors took the lead through Bradley Johnson at the Stadium of Light, but Lewis Grabban levelled things up from the penalty spot shortly before half time to send Sunderland into the break of their first Championship game for more than a decade all square.
Grabban almost added a second after the interval, but he was denied by the woodwork as the Black Cats' wait for a first home win of 2017 continued.
A plethora of summer signings were on show at the Stadium of Light as new Sunderland boss Simon Grayson handed debuts to no fewer than six players, with Billy Jones and Lee Cattermole the only survivors from the side which started the final game of last season.
It was Sunderland that got off to the brighter start, and they could have broken the deadlock as early as the 10th minute when George Honeyman was released through on goal, but his chipped finish was heading away from the target until Aiden McGeady met it at the back post. McGeady's own effort was then blocked by Wisdom before the danger finally passed when Grabban volleyed a follow-up effort over the bar.
Sunderland's promising start to the match came to a grinding halt when Derby scored the opening goal of the new season against the run of play just a minute later, though, with Johnson tucking home from close range after Johnny Russell had got the better of Brendan Galloway on the right flank.
The Rams only scored one goal in their opening seven fixtures last season, but they almost made it two in the first 20 minutes of this term when Huddlestone's drilled effort was spilled by Jason Steele and Jacob Butterfield was unable to convert the rebound.
Scott Carson was called into action at the other end for the first time shortly afterwards when the ball dropped kindly for Cattermole, and the Derby keeper pulled off a stunning reaction save to turn the Sunderland skipper's powerful strike over the crossbar.
Set pieces in particular seemed to be causing Derby problems, and they again failed to clear their lines from a free kick when Davies's header only made it as far as Grabban on the edge of the box and the striker lashed an effort narrowly over the bar.
The equalising goal finally arrived for the hosts with three minutes left of the first half after Butterfield lost his balance inside the area and was unable to prevent the ball from bouncing up against his arm. Grabban stepped up to the resulting spot kick and made no mistake, tucking his finish into the bottom corner for a debut goal.
It was only Sunderland's fourth goal in their last 11 matches at the Stadium of Light, but they almost added another in the opening stages of the second half when James Vaughan steered a shot inches past the post.
The hosts needed Cattermole to glance Richard Keogh's header away from underneath his own crossbar moments later, but they were back on the front foot soon enough and came within the width of the post of taking the lead shortly before the hour mark.
Cattermole pounced onto a loose pass from Johnson before playing a square ball to Grabban, who let it run across his body before unleashing a powerful strike which cannoned off the post.
McGeady then flashed a long-range strike wide of the target before Cattermole squandered Sunderland's last big chance, mistiming his volley from close range after being picked out in the middle by Grabban.
It was a similar story in the other penalty area in stoppage time when David Nugent completely missed his kick following a knockdown by Craig Bryson, and that proved to be the last sight of goal for either side as the match ended all square.
The result means that Sunderland have now gone 12 matches without a win at home in 2017, while they have not won on the opening day of the season for the past eight years.
Derby, on the other hand, are unbeaten on the opening day for the ninth season in a row, although they have still never won at the Stadium of Light and are now 11 matches without a victory against Sunderland home and away.