The Genk forward notched either side of a David Ben Dayan goal as Israel established a three-goal cushion at Ramat Gan national stadium before Denis Calincov's late consolation for the visitors.
The victory kept third-placed Israel two points behind second-spotted Greece, who were 5-2 winners over Latvia earlier this evening, ahead of Wednesday's final round of matches in Group Two.
Barda thought he had put his side ahead after 20 minutes when he headed home Gil Vermouth's right-wing cross, but his effort was chalked off by the referee.
The Moldova defence did not heed that warning, however, and Israel broke the deadlock with a similar move shortly afterwards, Barda nodding Vermouth's cross past Stanislav Namasco.
Victor Bulat and Calincov both had efforts saved by Dudu Aouate and then Yossi Benayoun cleared Veaceslav Sofroni's header off the goal-line as Moldova looked to get back on level terms.
Aouate did well to turn Sofroni's shot away for a corner but the equaliser was not forthcoming for the visitors and in the 65th minute they found themselves two down.
Tamir Chen headed down a corner and Etey Schechter got a touch before his Hapoel Tel Aviv team-mate Ben Dayan took the game beyond Moldova's reach by tucking in Israel's second.
Four minutes later, Barda scored his second of the night and his sixth of the campaign with a clinical finish to make it 3-0.
Two minutes into stoppage time, Calincov was given too much time and space inside Israel's half and made the most of his opportunity, blasting a low drive past Aouate to make the scoreline a little more respectable.