Tom Bayliss and Chey Dunkley were on target as Shrewsbury secured a deserved 2-1 victory over Burton Albion.
In front of 5,477 fans at the Croud Meadow, Bayliss and Dunkley both scored in the first half to put Town on the path to victory.
Mason Bennett netted a stoppage-time consolation for the visitors.
But Town were more than worthy of the points with keeper Max Crocombe making good saves to prevent Ryan Bowman and Dan Udoh from making the scoreline more emphatic.
The result means Taylor's side have won both their games at home this season following our opening-day victory over Cheltenham.
Head coach Matt Taylor made one change from the team that faced Stevenage on Saturday with captain Chey Dunkley coming in for Tom Flanagan at the heart of the defence.
Salop played in a 3-5-2 system with Ryan Bowman and Dan Udoh as the front two and Tom Bayliss, Taylor Perry and Nohan Kenneh in midfield.
Burton lined up in a 4-2-3-1 formation with Josh Gordon the lone striker. Mason Bennett was in the number 10 role with Mark Helm and Kgaogelo Chauke out wide.
Just minutes after the referee had blown his whistle for kick-off, Shrewsbury were 1-0 up.
Carl Winchester did brilliantly to drive down the line and find Taylor Perry who moved it onto Udoh. The striker then sent in a cross which Bayliss slotted home.
Just two minutes later, Burton almost equalised when Gordon went one on one with Marko Marosi, but the Slovakian stopped him with a brilliant block.
From that point on, the game proved quite cagey but with Town continuously pressing to find a second.
They almost got one just before the break when Winchester again did brilliantly to win the ball high before driving forward and finding Perry in the box.
The midfielder produced some lovely footwork to work himself into a position where he looked destined to score. But Ryan Sweeney slid in to produce an outstanding block which put the ball out for a corner.
From that corner, though, we doubled our lead with Dunkley producing a smart header at the back post to nod in Jordan Shipley's delivery.
The second half had little to offer until the 56th when Steve Seddon hit the bar for the visitors with a looping header.
Town’s first chance of the half was when Udoh darted into the box before hitting a powerful strike which forced a corner.
Soon after, Kenneh won the ball back with a great challenge before laying it off to Udoh whose low cross found Bowman, but his effort was blocked well by John Brayford.
Bowman had another chance seven minutes before the 90 when he got on the end of Joe Anderson’s diagonal ball before bringing it down and volleying it at Crocombe, forcing him into a save.
Burton did manage to score late on when Bennett bundled it over the line to create a nervy last couple of minutes, but Salop held on well to make it two wins from the opening three games.
Shrewsbury Town: Marko Marosi; Joe Anderson, Morgan Feeney, Chey Dunkley; Carl Winchester, Nohan Kenneh, Tom Bayliss, Taylor Perry (Elliott Bennett 88’), Jordan Shipley (Tom Flanagan 90+3’); Ryan Bowman, Dan Udoh (Mal Benning 82’)
Unused substitutes: Harry Burgoyne, Tunmise Sobowale, Travis Hernes, Harvey Watts
Burton Albion: Jamal Blackman (Max Crocombe), John Brayford, Steve Seddon, Adeji Oshilaja, Sam Hughes, Ryan Sweeney (Mustapha Carayol 86'), Joe Powell, Josh Gordon (Bobby Kamwa 61'), Mason Bennett, Kgaogelo Chauke, Mark Helm (Jake Caprice 86')
Unused substitutes: Rekeem Harper, Ciaran Gilligan, Tom Hamer
Attendance: 5,477 (213 away)
Referee: Scott Oldham