Brew, who won the World Cup alongside Dragons teammates Tom Isaacs and Tal Selley in Dubai last month, makes a competitive debut in his second spell at the region, having spent the 2006/07 season there on loan from the Ospreys.
Brew rejoined the Dragons from the Cardiff Blues in January, initially coming in on-loan until the end of the season before a one year permanent contract comes into effect from June.
Fellow Wales Sevens star Isaacs has withdrawn from the squad due to a hip injury, and joins a lengthy Dragons injury list of Rhodri Gomer-Davies, Adam Black, James Harris, Gareth Wyatt and Marc Stchrebina.
Welsh international Luke Charteris returns to the Dragons starting XV for the first time since the Six Nations, as do Hugh Gustafson, Hoani Macdonald and Richard Fussell.
Dragons coach Paul Turner has no illusions about the windy playing conditions at the Sportsground, where his side have not won since May 2004.
He said: “We are well aware of our record in Galway and what a difficult place it is to go to.
“Connacht have already beaten Leinster and Munster at home this season and probably two or three of the regional sides have been on the brink of defeat there.”
Turner added: “This game will be a good challenge for us and our development if we want to move up the table.
“If we have any pretence of going into the top four in the Magners League we have to win in Galway.”
Michael Bradley makes four changes to his Connacht side, with centre Niva Ta’auso and scrum-half Frank Murphy both overcoming injuries to return in the backline.
Up front, prop Ronan Loughney and flanker Johnny O’Connor come into the side. There are also a number of positional changes from last Friday’s 32-5 loss at Edinburgh, as Gavin Duffy switches from the centre to full-back, Andrew Browne moves into the second row and Ray Ofisa makes his first start at number eight.
Dragons Kevin Morgan, Richard Fussell, Rory Sidey, Ashley Smith, Aled Brew, Jason Tovey, Wayne Evans, Hugh Gustafson, Tom Willis (Capt), Rhys Thomas, Sean Tomes, Luke Charteris, Hoani Macdonald, Richard Parks, Joe Bearman,
Replacements Steve Jones, Nigel Hall, Adam Jones, Danny Lydiate, Martyn Thomas, Shaun Connor, Robert Lewis,
Connacht team: G Duffy; F Carr, N Ta’auso, K Matthews, L Bibo; I Keatley, F Murphy; B Wilkinson, S Cronin, R Loughney; A Browne, A Farley; J Muldoon (C), J O’Connor, R Ofisa.
Replacements: A Flavin, B McGovern, M Swift, C Rigney, C O’Loughlin, A Dunne, T Nathan.