The Queenslander's unbeaten 103 helped the tourists to a competitive total after they elected to bat on a slow pitch difficult for strokeplay.
Symonds, who came in at the fall of three quick wickets, added 140 for the fourth wicket with Michael Clarke (54) as Australia looked to take a decisive lead in the three-match series.
The world champions lead 1-0 after a four-wicket win in the first match in Chittagong on Sunday.
Symonds, who began cautiously, opened up later to smash six fours and two sixes in his fifth hundred in 145 matches.
Clarke was content to nudge the ball for singles during his 18th half-century, hitting just two fours off 90 balls before he was caught by Alok Kapali in the covers off spinner Mohamad Rafique.
Australian vice-captain Adam Gilchrist had earlier got the team off to a flying start but fell when he looked set for another big knock.
Gilchrist, who had scored a match-winning 76 in the first match, scored 32 off 30 balls with a six off paceman Mashrafe Mortaza and four boundaries.
But Mortaza then engineered a mini-collapse, bagging three wickets in the space of 10 deliveries.
He trapped Gilchrist leg-before, clean-bowled captain Ricky Ponting (five) and had left-hander Simon Katich (26) caught by Shahriar Nafees in the covers as the Aussies slipped from 55-0 to 65-3.