It was a poor start for Bournemouth as Hodkin tapped home in the opening five minutes, but a Michael Dacosta Gonzalez strike from range drew the hosts level.
Alan Connell’s side were the better of the teams for the remainder of the first half, but couldn’t find a second goal, and they went behind in the opening exchanges of the second period.
But they responded well to going behind again, and Eugene Nyarko headed them level before Day finished well from a tight angle to seal the victory for the hosts in the dying minutes.
The visitors took the lead with the first chance of the game.
Luca Moore fired towards goal and Kai Crampton got down to save, but he could only parry across the six yard box which left a simple tap in for Jordan Hodkin.
Crewe were on top in the opening exchanges after their goal and had plenty of possession around the Bournemouth box.
But they weren’t able to convert their early spell into chances and the Cherries were back level after ten minutes.
It was a brilliant strike from Dacosta Gonzalez as he picked the ball up in space and beat a man, before he fired into the bottom corner from the top of the D.
Bournemouth threatened next through Koby Mottoh as he clipped shot went just wide of the top corner, after good work from Remy Rees-Dottin on the left.
The Cherries were now in the ascendancy.
Rees-Dottin shot off target before Dacosta Gonzalez caused more problems for the Crewe defence on the edge of the area, but Day couldn’t quite work space for a shot when it was poked through to him.
Mottoh beat both Charlie Finney and Shilow Tracey on the left and stood a good cross up for Alfie Merritt, but Tom Booth caught comfortably.
Day then shot wide moments later, before Dacosta Gonzalez put in a dangerous cross to the back post, but Eugene Nyarko could only flick wide with his head.
Charlie Stevens shot tamely at Booth as the Cherries sought the lead before the break, but the sides went into the interval level pegging.
Crewe had an early chance as Crampton saved well from Hodkin, before Rees-Dottin fired just wide from the centre of the box after he was found by a Stevens pass.
Isaac Irwin nearly turned a cross from the left from Merritt into his own net, before Owen Taylor shot wide for Alexandra.
A brilliant corner routine from the visitors nearly saw them edge in front, as Taylor dummied for Luca Moore to strike it from just outside the D, but he struck the woodwork and it bounced to safety.
Crewe were on top in the opening exchanges of the second period, and Hodkin headed over from a free kick before the visitors took the lead.
Dion Rankine was played in on the left and played a short pass to Moore, who showed some neat footwork to turn in the box and finish into the bottom corner.
The Cherries had a shout for a penalty waved away when Nyarko went in on goal and was challenged by Irwin, as they sought an equaliser.
Rees-Dottin shot over the bar when he teed himself outside the box, before Crampton had to be at his best to deny Moore a second.
The Bournemouth winger went down in the box and again referee Craig Barnett waved the penalty shouts away.
Nyarko drew a good save out of Booth from close range as the Cherries started to turn the screw.
Booth made an excellent double save to save from Dacosta Gonzalez from range and then Day as he followed up and sought to prod home the rebound.
The Crewe keeper was on top form and again denied Bournemouth. This time it was Mottoh who cut in from the right and looked to finish, but the stopper tipped it over the bar.
But Booth could do nothing to stop Nyarko’s header as the Cherries took the resulting corner short and the forward rose to meet Zac Christie’s ball in to make it 2-2.
Noa Boutin replaced Christie after the goal, before Finn Tonks and Rees-Dottin came off for Ethan Sills and George Chubinidze.
Nyarko headed wide as the game entered the final five minutes, and the Cherries snatched the lead in the 88th minute.
Day was slid through by Nyarko and he finished brilliantly from the angle to make it 3-2 to the hosts.
Crewe went after an equaliser and Lucas Swann hit the post from a Thomas Graves cross.
Nyarko had an effort blocked after a good run from Chubinidze and the Cherries held on to win all three points to stay second in the Professional Development League south group.