The man who spent a season at the New Bucks Head back in 2014, handed his side a first half lead with a tap in on 18 minutes, before striker Daniel Udoh grabbed his 13th goal of the campaign to level it up.
Telford struggled to create any real clear cut chances against their in form hosts, who got back in front 16 minutes from time thanks to a superb curling free kick from Connor Hampson.
They tried to rally without testing Alty's defence, and the game was put to bed two minutes from time as Hancock grabbed his second of the afternoon.
The game passed an 11am pitch inspection, but even after the Bucks arrived at the ground the game remained in doubt.
Referee Benjamin Speedie took to the field 45 minutes before kick off, testing the roll of the ball on the surface.
He deemed it playable, shortly before the heavens opened again to make the sodden surface even damper.
Gavin Cowan said his troops were not good enough in last week's first home defeat of the season and he opted to make two changes against one of the league's form sides.
Shrewsbury Town loanee Ryan Barnett impressed enough in his 30 minute spell from the bench last week to warrant a start.
He replaced Amari Morgan-Smith, with Dom Smith missing out as defender Theo Streete returned from suspension.
The game got under way in what could only be described as testing with the rain lashing down, and the ball holding up a number of areas of the pitch.
If the rain had got any heavier, referee Speedie may have been forced into a decision. As it was, the rain stopped but the surface remained difficult.
The first half chance of the game went to Telford, with Barnett firing over from the edge of the box after being found by Daryl Knights.
The water on the surface was hampering proceedings, and played a part in Altrincham taking the lead with their first real chance on 18 minutes.
The ball held up on the surface during a Bucks move, leading to the hosts pinching possession and breaking.
A cross field ball was misjudged by Ross White, allowing John Johnston to skip past him and drive towards goal.
The winger avoided Shane Sutton's lunging tackle, before squaring for Hancock to tap home from six yards.
It was almost two soon after, but the returning Streete denied striker Jordan Hulme just as he was about to pull the trigger after driving into the box.
Following that chance the Bucks went straight up the other end and drew themselves level, as Udoh ended his recent dry spell in front of goal.
Barnett's cross from the right was met by Ellis Deeney at the back post, and his blocked header fell to Udoh who fired home from close range through a cluster of Altrincham bodies.
Both sides were trying to play passing football, but the surface wasn't particularly helping, especially down one flank with the ball continually holding up throughout the half.
Connor Hampson lashed wide from the edge of the box for the hosts on 34 minutes, but apart from the goals neither goalkeeper was really tested in the first period despite both sides enjoying spells of pressures.
Ten minutes into the second half though and Andy Wycherley was called into action for the first time, producing a superb low save to keep the scores level.
Hulme climbed highest to meet Johnston's cross from the right and his glancing header looked to be nestling in the corner, but the Bucks stopper got down well to tip it around the post.
A couple of dangerous looking crosses down the other end were easily cleared by the Alty defence, before Wycherley was called into action again 20 minutes from time.
Hulme's through ball found Kallum Mantack who went bearing down on goal, but the keeper rushed off his line to deny the winger.
The hosts had the momentum in their favour, and they managed to make their sustained spell of pressure pay 16 minutes from time.
Mantack skipped inside and found Shaun Densmore on the edge of the box, who was upended by Deeney.
Left back Hampson stepped up and fired a free kick over the wall and into the corner of the net, leaving Wycherley with absolutely no chance.
Manager Cowan responded immediately, turning to his bench and introducing loanees Brendon Daniels and Yusifu Ceesau in a bid to snatch a later equaliser.
But Altrincham had a firm grip on the game in the latter stages, and Hancock put the game beyond all doubt two minutes from time.
The ball worked its way to Ashley Hemmings, whose smart pass in the box found the unmarked Hancock who slotted past a helpless Wycherley.
18 - GOAL - A cross field ball is misjudged by Ross White, allowing John Johnston to skip past him and then Shane Sutton, before squaring for former Buck Josh Hancock to slot home.
25 - GOAL - Ryan Barnett's cross finds Ellis Deeney who sees his header blocked. But Daniel Udoh is on hand to fire the ball in through a cluster of home defenders.
57 - SAVE - Andy Wycherley is called into action for the first time, getting down low to tip Jordan Hulme's header wide. Looked to be a certain goal and nestling in the corner but the Bucks stopper did well.
69 - SAVE - Wycherley has to be quick off his line to deny Kallum Mantack following a through ball from Hulme.
74 - GOAL - Nothing the keeper could do about this one though. Deeney takes down Densmore on the edge of the box, and Hampson steps up to curl a free kick over the wall and in.
88 - GOAL - Ashley Hemmings finds Hancock in the box and he slots home to put the game beyond doubt.
Altrincham (4-5-1) - Thompson, White (Densmore 12), Hampson, Jones, Hannigan, Moult, Johnston (Harrop 85), Richman, Hulme, Hancock, Mantack (Hemmings 76)
Subs not used - Langley, Wynne
AFC Telford United (3-5-2) - Wycherley, White, Deeney, McQuilkin (Daniels 80), Sutton, Streete, Cowans, Royle (Ceesau 83), Barnett (Morgan-Smith 70), Udoh, Knights
Subs not used - Smith, Brown
Referee - Benjamin Speedie
Attendance - 895