Bay of Plenty started well, stealing the first lineout feed from Auckland, and scoring through blindside flanker Shahn Eru from an impressive lineout drive. Kelly Haimona slotted from the touchline.
Simon Hickey kicked a penalty for Auckland but after the Steamers again stole the ball off an Auckland lineout, Stanaway scored after a fine break by Tupe.
The player many pick to be a long-term All Blacks centre in Rieko Ioane then scored a superb individual try from 55 metres out for Auckland.
Back came the Steamers with a trademark lineout drive which again Tupe finished off to regain the lead before Lolagi Visinia and Ioane scored to put Auckland 25-19 ahead at the break.
Hickey opened the scoring in the second stanza with a charge-down try after his opposite Haimona took too long to clear.
When Ioane cut through to score his third try Auckland had raced away to a 39-19 lead after 52 minutes but the Steamers came storming back with fresh legs from the bench.
Tupe crashed over for his second try and they came close from five more raids at the Auckland line, including what looked a sure penalty try not given from a pushover scrum.
Finally, Tupe scored from the back of another excellent Steamers scrum for his seventh for the season. The conversion closed the gap to six points with 12 minutes left.
Auckland scored immediately through fullback Melani Nanai but the never-say-die Steamers powered back on attack with Stanaway scoring his second try to set up a thrilling final three minutes.
Tupe started a final phase of play that resembled an overcrowded game of sevens but Auckland's defence held on to take the points.
Steamers captain Culum Retallick was prominent in his 99th game in the blue and gold hoops with a special occasion to come next Saturday against North Harbour in Albany.
Auckland 44 (Rieko Ioane 3, Lolagi Visinia, Simon Hickey, Melani Nanai tries; Simon Hickey 4 con, 2 pens)
Bay of Plenty 38 (Joe Tupe 3, Teddy Stanaway 2, Shahn Eru tries; Kelly Haimona 2 cons; Dan Hollinshead 2 con) HT 25-19
