Adelaide recovered from a 26-point deficit early in the second quarter to log a 15.13 (103) to 15.12 (102) victory at Adelaide Oval on Saturday night.
The Crows move to three wins and three losses and ninth spot on the ladder while leaving the 13th-placed Saints (two wins, four defeats) in early strife.
Walker and Riley Thilthorpe (three goals) were dangers in attack and teammates Wayne Milera (29 disposals) and Josh Worrell (28, 11 marks) standouts in defence.
"Tonight was one where we guts it out and actually executed some really high quality stuff towards the end of that game, which our guys will learn from," Crows coach Matthew Nicks said.
St Kilda's Jack Sinclair collected a game-high 35 possessions, Jack Higgins kicked four majors, and Nasiah Wanganeen-Milera (28 touches), Callum Wilkie (31, 11 marks) and Darcy Wilson (24, two goals) were influential.
"I couldn't be prouder of the fight," Saints coach Ross Lyon said.
"Our best is very good, but we need more consistency."
After Adelaide's Ben Keays kicked the opening goal 90 seconds in, the Saints took complete control.
Sinclair amassed 17 disposals, Wilkie had 13 and took six marks, and  Higgins slotted two goals as the visitors raced to a 4.4 to 1.2 quarter-time lead.
St Kilda's advantage stretched to 26 points early in the second quarter but the tide then turned drastically.
The Crows booted seven goals - six consecutively - to one in a powerful retort to create an eight-point halftime lead, 8.4 to 6.8.
Adelaide's spree extended into the third stanza with the 35-year-old Walker slotting two goals in four minutes.
And his teammate Brayden Cook (19 disposals, seven inside 50s) threaded a stunning checkside goal from near a boundary line to put Adelaide 27 points up - and the Saints on the ropes.
But the visitors responded with the next two goals, only for imposing Crow Thilthorpe to snag two quick majors as the hosts stretched their break to a game-high 29 points.
Yet again the Saints rallied, with Higgins' third and a post-siren conversion from Tom De Koning reducing their three quarter-time deficit to 15 points.
St Kilda scored the initial three goals of the final term to level scores with a dozen minutes remaining.
Adelaide's Keays snapped accurately with a tick over six minutes left, giving the home side a seven-point cushion - only for Higgins to boot his fourth: the Saints were one point down with four minutes left..
But after scores were again tied, an Alex Neal-Bullen point for the Crows was followed by Walker's fifth with a classy left foot snap.
Saint Mitch Owens goaled with 10 seconds left but his side fell agonisingly short.
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