The promotion-chasing Magpies looked down and out after Lewin Nyatanga and Nicky Maynard fired the hosts into a commanding lead at the break.
But a mistake from the otherwise flawless Robins goalkeeper Dean Gerken allowed Jonas Gutierrez to reduce the deficit before Andy Carroll levelled with his 15th goal of the campaign.
The match ended a week that saw Gary Johnson part company with the Bristol club after four-and-a-half years at the helm, and caretaker boss Keith Millen described the visit of the Magpies as "the perfect game" to kick off with.
Liam Fontaine was ruled out as Millen opted for a 3-5-2 formation, with Christian Ribeiro coming into the side alongside Louis Carey and Nyatanga in a back three.
With Jamal Campbell-Ryce suspended, Maynard and Danny Haynes got the nod up front.
Newcastle boss Chris Hughton had a simpler task, with Leon Best in for the injured Peter Lovenkrands being the only change to the side that beat Scunthorpe in midweek.
City began brightly and Haynes headed Bradley Orr's cross onto the roof of the net before United defender Fitz Hall had to block another Haynes effort.
The home side's early pressure was rewarded when Paul Hartley tapped a free-kick to Maynard 22 yards from goal. His rasping shot was too hot for Steve Harper to handle as he fumbled and allowed Nyatanga to slot in the rebound for his first City goal.
Newcastle's first sign of goal came when Gutierrez crossed for Carroll but the big frontman headed narrowly over the top when he should perhaps have done better.
City survived a scare when Nyatanga sliced horribly in his own box but a combination of Gerken and Carey blocked Best's volleyed effort.
Gerken was also alert as half-time approached, Best nodding the ball back across goal for Kevin Nolan who could only head the ball straight at the former Colchester man.
Newcastle were made to pay minutes later when Maynard doubled the advantage in style.
Orr launched a ball over the top that the frontman did well to keep in play on the left wing, before cutting into the penalty area where he curled the ball into the far corner at pace past a helpless Harper.
Hughton's men thought they had reduced City's lead in added time when Danny Guthrie went round Gerken and tried to slot home but Hartley darted in at full throttle to keep the shot out.
Millen made a change at half-time with Jamie McAllister, who was booked in the first half, replaced by Evander Sno and the substitute tested Harper soon after.
Hall made way with a knock in the 50th minute with Tamas Kadar coming on and he forced Gerken into a stop as the rain came down at Ashton Gate and the ball fizzed off the surface.
Wayne Routledge sent a 70th-minute effort into orbit as Newcastle searched for a way back into the game and Gerken thwarted Gutierrez's rasping effort.
But seconds later the Argentinian made Gerken pay for a slip, the stopper innocently rolling the ball out to Cole Skuse before Gutierrez nipped in on the blindside to roll the ball in.
Newcastle were level 15 minutes from time when Carroll swept in Routledge's pass and the momentum was firmly with the league leaders.
Gerken made amends with a fingertip side to deny Best as Newcastle upped the ante but they failed to find a late winner and sit two points clear at the top with a game in hand on second-placed West Brom.