The defender lashed home after 82 minutes to see off determined Aldershot Town at the Wessex Stadium.
The former Leyton Orient star beat Shot keeper Nikki Bull from close range following Abdou El Kholti's dangerous corner from the right.
His winner sent the home fans into a understandable frenzy given they have waited 17 years for top-flight non-league football.
Downer struck in the weekend win at Tamworth and was at it again in front of a packed Radipole Lane crowd who have been starved of success for so long.
Defeat was harsh on the spirited visitors who looked sharp all night but were lacking in attack.
But that won't worry Terras boss Gary Hill, whose experienced side look a good bet for the play-offs on this showing. Weymouth chairman Martyn Harrison has spent big on the South coast to assemble a squad packed full of Conference experience.
Meanwhile his Shots counterpart Terry Brown will be concerned at how his charges failed to seriously test home goalkeeper Aaron Lee-Barrett.
After the opening day success at Tamworth, Terras boss Hill understandably kept faith with same starting 11 on duty in the Midlands.
Having been starved of Conference football for so long, the hosts began nervously with the shot quicker off the mark.
Lively visiting winger Ryan Williams saw his fifth minute cross half cleared to Ricky Newman whose tame volley trickled wide.
Shots strike pair John Grant and Marcus Gayle then combined for the latter to send Terras keeper Lee-Barrett sprawling to his right to save.
Weymouth slowly but surely found their feet though and only the shins of Shots keeper Bull denied Lee Elam.
Lone striker Raphael Nade then nearly capitalised on a mix-up in the visitors defence but his shot lacked power.
With first-half chances at a premium, it was the former Woking striker Nade who looked the host's most likely source. The Carlisle United asset, on a season-long loan at the Wessex Stadium, then set up midfielder Simon Weatherstone whose effort flashed just over.
For their part, Aldershot were struggling to fashion any openings although towering striker Grant did go close on 32 minutes. The ex-Halifax Town star got on the end of Darren Barnard's dangerous corne,r but his header crashed into Lee-Barrett's side netting.
Weymouth opened the second period brightly. but could not find a way through a resolute Shot rearguard. When Terras dangerman Nade did battle his way into the area, on 52 minutes he wildly sliced his shot well wide.
The visitors were cursing their luck on the hour when the excellent Williams again drifted in off the left to set up Grant.
The striker took a touch and with space opening up, sent a curling effort just wide.
Moments later Grant looped a close-range header against the Terras crossbar, before the Shots wasted another golden opportunity midway through the half.
Louis Soares scampered down the right, picked out Williams six yards out but the midfielder somehow failed to hit the target.
Home boss Hill responded by replacing striker Chukki Eribenne with substitute Richard Logan and the switch nearly proved inspired.
The former Peterborough United striker thought he had scored the winner when he headed goalwards with minutes remaining, only to see Bull pull off a tremendous reflex save.
Then came Downer's dramatic winner to spark wild celebrations among the home fans.