Betts kicked five goals and Podsiadly one as the Crows thumped Port 0.18.11 (119) to 0.9.5 (59) at Richmond Oval.
Ex-Carlton forward Betts kicked goals with his first two kicks for the Crows.
And former Geelong attacker Podsiadly booted a major after his first mark for Adelaide, and then created the next goal, before being swung into defence later in the game.
The big-name signings featured in five of Adelaide's initial six goals against a Port side missing a dozen proven performers.
Port's acting captain Angus Monfries was the only member of the Power's eight-strong leadership group to play.
And Port's two best forwards (Chad Wingard and Jay Schulz), two best backmen (Alipate Carlile and Jackson Trengove) and best ruckman (Matthew Lobbe) also didn't play.
The class gap was obvious as Adelaide scored the initial seven goals before a crowd of 8765 spectators.
Port, who didn't muster a major until Aaron Young's goal 12 minutes into the second, trailed by 51 points at halftime.
And the Crows stretched their lead to 76 points midway through the third term after Betts slotted another couple of goals.
Port kicked five of their goals in the final term, but the damage was done.
Betts was outstanding while onballers Richard Douglas (two goals), Matthew Wright (two goals), David Mackay and newcomer Matt Crouch were influential.
In contrast, Port struggled for winners with Young, Andrew Moore and veteran Dom Cassisi all battling hard while prized recruit Jared Polec was eye-catching in patches.
ADELAIDE 0.5.2 0.10.7 0.16.8 0.18.11 (119)
PORT ADELAIDE 0.0.2 0.2.4 0.4.4 0.9.5 (59)
Nine pointers: Adelaide - Nil. Port Adelaide - Nil.
Goals: Adelaide - Betts 5; Wright, Douglas 2; Smith. Jenkins, Lyons, Podsiadly, Porplyzia, Johnston, Sloane, Kerridge. Port Adelaide - Young, P Stewart 2; Newton, Pittard, White, Logan.
Best: Adelaide - Betts, Douglas, Wright, Mackay, Crouch, Sloane. Port Adelaide - Young, Moore, Broadbent, Polec, Stevenson.
Umpires: Sam Hay, Leigh Haussen, Craig Fleer.
Venue: Richmond Oval.