The striker, on loan from Chelsea, struck seven minutes before the break in Saturday's St James' Park clash to cancel out the lead former Wanderers midfielder Kevin Nolan had given the Magpies with his 11th of the season with 13 minutes gone.
But an open game shifted firmly Bolton's way with Ryan Taylor's 54th-minute dismissal for a two-footed challenge on Johan Elmander.
Taylor was making just his fifth appearance of the season on his return from an ankle ligament injury, but his rush of blood left Newcastle hanging on for a dear life.
The draw ended Bolton's run of six successive Premier League away defeats and extended the Magpies' run to one loss in nine.
In Sturridge, Bolton had a deserving candidate for man of the match as he caused problems for the off.
Fabricio Coloccini repeatedly needed the help of full-back Jose Enrique to keep the striker at bay, although the Spaniard had his own hands full with Elmander, who caused such problems during the Magpies 5-1 defeat at the Reebok Stadium in November, playing in a wide midfield role.
But Newcastle gave as good as they got in a thrilling first half, during which play switched rapidly from end to end.
The home side took the lead with 13 minutes gone, and yet again, it was Nolan who did the trick.
Not for the first time, he demonstrated his knack of finding space inside a crowded penalty area to meet Cheick Tiote's driven cross, and his deft header was too good for Jussi Jaaskelainen.
The Finn had kept out Peter Lovenkrands' near-post flick seconds earlier, and later needed David Wheater's help to prevent Leon Best's shot ending up in the back of the net.
Best headed a Taylor free-kick just over the bar with 28 minutes gone. The former Wigan man was a late replacement for Joey Barton, who suffered an injury during the warm-up.
Only a last-ditch tackle by full-back Marcos Alonso denied Taylor seconds later - but Sturridge continued to look the man most likely to drag Bolton back into the game, and he did just that seven minutes before the break.
A rare mistake from Tiote allowed Elmander to find the striker, and he shifted the ball on to his left foot before shooting unerringly into the bottom corner.
Lovenkrands helped a Tiote effort just over the bar and Nolan bravely blocked an Elmander drive as the half drew to a close.
Jaaskelainen was back in action within three minutes of the restart after Enrique spun away from Elmander with ease before surging into the penalty area and unleashing a powerful shot.
However, Alonso fired over from 20 yards and Steve Harper had to get down well to claim Gary Cahill's deflected drive as Bolton responded.
But the momentum shifted significantly with 54 minutes gone when Taylor launched himself at Elmander and was dismissed by referee Chris Foy, who had little choice but to produce the red card.
Bolton instantly sensed an opportunity and committed more men to the search for a winner, and Coloccini and Mike Williamson found themselves firmly in the firing line as they were forced to deal with a series of dangerous crosses.
Lovenkrands dropped into the wide midfield berth vacated by Taylor to leave Best alone up front, and there was little the former Coventry man could do to help stem the tide.
Magpies boss Alan Pardew made his move with 23 minutes remaining when he sent on central defender Steven Taylor for Jonas Gutierrez and striker Nile Ranger for Lovenkrands, and went to a back three.
Ranger headed over from Taylor's 70th-minute cross, but it took a priceless goal-line clearance from Nolan to keep out Martin Petrov's effort five minutes later.
There was late drama when Jaaskelainen had to scuttle across his line to collect the ball after Paul Robinson had chested Best's cross a little too firmly towards goal.