After a bright start, it was DPMM who broke the deadlock in the 38th minute, Basiru Osman scoring with a header.
A patient Tampines side failed to draw level until the 48th minute when a thunderous Mustafic Fahrudin freekick from 25 yards out found the back of the net.
DPMM surged forward in search of another, and they were rewarded for their attacking intent on 69 minutes when Croatian midfielder Ivan Jerkovic beat Tampines goalkeeper Sasa Dreven with a fine strike from outside the penalty box.
Not to be outdone, Tampines veteran Jamil Ali latched onto a rebound off DPMM's goalkeeper Wardun Yusoff in the 90th minute and cleverly flicked the ball into an empty net to ensure his team headed back home with a point in the bag.
Brunei DPMM coach Vjeran Simunic said: "I am happy with the one point gained today [Sunday] and I feel that it was a deserving game for both teams.
"I will now have to see the injuries we sustained tonight [Sunday] and prepare for the next match. I am looking forward to the match against SAFFC. After missing out on football for three years, we are glad to be back in the S.League."
Tampines Rovers FC Coach Steven Tan added: "It was a good game and I believe that my players showed the character needed to match the opponents.
"They were overawed by the crowd in the first half but they got their nerves under control and came back well in the match.
"Tonight's [Sunday's] attendance is a good advertisement for football and I hope we can follow it up back in Singapore."
DPMM FC: Wardun Yusoff, Siarol Sahari (Suhaime Yussof 89'), Tales Dos Santos, Shahrulrizal Abd Rahman (Helmi Zambin 83'), Azwan Saleh, Ivan Jerkovic, Rodrigo Grahi, Subhi Abdilah, Rosmin Kamis, Basiru Osman, Shahrazen Said.
Tampines Rovers: Sasa Dreven, Ismadi Mukhtar, Jufri Taha, Mustafic Fahrudin, Davor Piskor (Ahmed Fahmie 82'), Aleksandar Duric, Imran Sahib, Anaz Hadee, Gligor Gligorov (Ali Hudzaifi 73'), Benoit Croissant, Jamil Ali (Hairul Nazri 90').