For "underdog" consultancies, i've always felt that they win by
1) sending their A team where an incumbent would be sending in their C team. That would make sense, as the incumbent's A team is on a more important client, whereas this small client "is" the underdog's important client.
2) carving out niches and specialties. So you serve less clients and projects, but also build up a reputation. You kind of become an incumbent of sorts, just for that niche.