A season-ending injury to top scorer Charlie Austin forced Rangers boss Redknapp into a familiar deadline-day scramble for new recruits, and two of them had an instant impact.
Wolves striker Doyle and West Ham flop Maiga had scored just four league goals between them this season, but the new loan signings grabbed one apiece to keep Rangers in second spot, three points ahead of the Clarets.
"Harry is shrewd when it comes to dealing in the transfer market and he has an amazing instinct for these things," said assistant manager Kevin Bond.
"He can almost sniff out a player and I hope he's proved right again.
"Maiga for whatever reason wasn't doing himself justice at West Ham, but both Harry and I had seen him play and Harry felt he had a little more to offer than he has shown.
"What you know you will get from Kevin Doyle is a stint, he will chase lost causes and we need that energy. Hopefully that goal will do him the world of good."
In contrast to Redknapp's hastily-assembled frontline, Burnley strikers Danny Ings and Sam Vokes are in stunning form.
The dynamic duo took their combined tally for the season to 37 goals - one more than Rangers have managed in total.
Ings swept home a superb equaliser after Doyle opened the scoring with a powerful header, before the unlikely figure of Richard Dunne volleyed Rangers into the lead at half-time.
But Vokes hauled Burnley level when he prodded in Michael Kightly's cross and Ings capitalised on a slip from Benoit Assou-Ekotto to tee up his strike partner for the third.
However, Maiga climbed off the bench to tap home a precious equaliser from Junior Hoilett's cross with 12 minutes left.
"It's not like us to score three and concede three at home," added Bond.
"It was a hard game, Burnley are a good, well-organised side and their front two are a constant threat.
"They will be there or thereabouts at the end of the season, hopefully with us."
The Clarets missed the chance to climb above Rangers on goal difference but they certainly look like a team who can go the distance in the promotion race.
"We've now taken four points off the pre-season promotion favourites and that's a good marker for us - we are up there for a reason," said manager Sean Dyche.
"We've found a good mixture this year, good energy, good tempo and real quality.
"Ings and Vokes are a very good partnership and very good individually. They have quality and the desire to work hard for the team.
"I was disappointed with the goals we let in, but then I'm sure QPR are disappointed with the goals they conceded as well."