Andy Goode looked to have secured victory for the Warriors just two minutes earlier after Gloucester skipper Jim Hamilton recklessly pushed Worcester lock James Percival at a lineout.
But Worcester could not hold on, and substitute Burns struck with the final kick of an otherwise dire contest to secure a draw.
Gloucester centre Henry Trinder and Worcester replacement prop James Currie scored second-half tries, while Goode slotted two penalties and his team-mate Joe Carlisle a penalty and conversion.
Burns, who went on in the second period, slotted a penalty and conversion from his two kicks at goal and there was a penalty double from Billy Twelvetrees, but neither side covered themselves in glory.
Conditions were ideal for a free-flowing spectacle, yet both teams' repeated failure to master basic handling skills helped render the game largely a non-event.
Scotland wing Nikki Walker made his Worcester debut after moving to Sixways from the Ospreys earlier this year, while there were first Gloucester starts for wing Shane Monahan - who replaced an injured Charlie Sharples - and Australian hooker Huia Edmonds.
Twelvetrees found his range inside the opening two minutes, landing a 50-metre penalty that served notice to the Warriors he meant business.
Goode slotted an equalising strike 10 minutes later, although only after he required lengthy treatment following a crunching tackle by Gloucester scrum-half Dan Robson.
Despite a perfect playing surface, both sides struggled to string together meaningful attacking phases and Gloucester regained the lead through another Twelvetrees penalty.
Goode, who stayed on in an attempt to run off his knock, missed two penalties but Worcester should have scored from their first notable attack.
Former England forward Chris Jones shrugged off a couple of weak Gloucester challenges to power towards the line, yet visiting full-back Jonny May executed a stunning tackle that ensured Gloucester retained their lead.
The Warriors attempted to free Samoan wing speedster David Lemi at every opportunity, and although Gloucester marshalled him well, Worcester looked a more threatening attacking unit.
But Goode did not help his team's cause when he was sin-binned after taking out Trinder off the ball, and the visitors piled on pressure as half-time approached.
Wing James Simpson-Daniel was guilty of a woeful blunder when he failed to gather possession with Worcester's line at his mercy, yet 14-man Worcester somehow held out under intense pressure, trooping off just three points adrift.
Carlisle took over kicking duties while Goode served his 10-minute spell on the sidelines, and an angled penalty success made it 6-6 in a game that badly needed some inspiration.
Gloucester boss Nigel Davies made his first substitutions just 13 minutes into the second period, one of which included Burns replacing Mike Tindall and Twelvetrees reverting to his more familiar inside centre position.
Burns, who scored 39 points in Gloucester's opening two league games against Northampton and London Irish, looked to make an immediate impression on the contest.
He mixed his kicking game well but errors abounded around him until Gloucester struck with the game's first try 14 minutes from time.
Monahan made it possible through a powerful touchline burst and, as Worcester defenders desperately scrambled back, the ex-Rotherham player's well-timed pass sent Trinder sprinting over.
Burns converted but Worcester stirred to set up a gripping finale the game hardly deserved when Currie ploughed over for a try that Carlisle improved.
Gloucester found themselves stretched defensively for the first time and Worcester entered the final five minutes pushing hard to turn territorial dominance into points.
The victory they coveted looked to have arrived deep into injury time when Goode kept his nerve under intense pressure, but then Warriors' front-row infringed and Burns made it 16-16 with the game's final kick.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.