Wednesday had a penalty appeal turned down when Richard Keogh appeared to handle Adam Reach's shot on the line.
Christie then met a Tom Ince corner to nod Derby ahead from close range.
Liam Palmer went closest to a leveller, with a deflected shot off the post, before Alex Pearce prodded home Derby's second from eight yards.
Steve McClaren's Rams moved up three places to 18th in the Championship table with their second win in four games since the former England manager returned as Derby boss.
Kieran Lee was first to test Derby goalkeeper Scott Carson, and Fernando Forestieri was also kept out before the penalty shout on nine minutes.
Christie, among Derby's most industrious players along with Ince and Jamie Hanson, netted the opener and ensured the home side led at half-time in a match for just the second time in all competitions this season.
Palmer and Forestieri threatened for the Owls before Pearce pounced on a deflected shot from Jacob Butterfield to make it 2-0, with Wednesday - beaten for the first time in three matches - suffering further as Steven Fletcher was forced off following a head knock just 16 minutes after coming off the bench.
REACTION: Derby boss Steve McClaren speaks to BBC Radio Derby
Derby manager Steve McClaren:
"Keogh made a great save without his gloves on and we rode our luck in that.
"Game's are turned on that one way or another and it turned our way and what you have to do in those instances is take advantage and that's what we did.
"It's a huge win, we said put a marker down at five o'clock and they've done that. There were aspects of the performance that improved immensely and we created chances as well."
Sheffield Wednesday head coach Carlos Carvalhal on Adam Reach's penalty appeal:
"In my opinion, it's the worst decision in the Championship so far. I have seen nothing like it this season.
"I have nothing against the ref, nothing against the person but the decision was very, very poor and it had a big impact on the game.
"People talk a lot about how we need technology but why do we need a camera or a video when we have three referees on the pitch, one of them must see it. They have communication and can say it's a clear penalty."
Match ends, Derby County 2, Sheffield Wednesday 0.
Second Half ends, Derby County 2, Sheffield Wednesday 0.
Offside, Derby County. Matej Vydra tries a through ball, but Jacob Butterfield is caught offside.
Foul by Tom Lees (Sheffield Wednesday).
Matej Vydra (Derby County) wins a free kick on the right wing.
Substitution, Derby County. Max Lowe replaces Johnny Russell.
Attempt missed. Bradley Johnson (Derby County) left footed shot from outside the box is close, but misses to the left. Assisted by Ikechi Anya.
Sam Hutchinson (Sheffield Wednesday) wins a free kick in the defensive half.
Foul by Matej Vydra (Derby County).
Atdhe Nuhiu (Sheffield Wednesday) is shown the yellow card for a bad foul.
Foul by Atdhe Nuhiu (Sheffield Wednesday).
Johnny Russell (Derby County) wins a free kick in the attacking half.
Attempt saved. Matej Vydra (Derby County) header from the centre of the box is saved in the bottom right corner. Assisted by Johnny Russell with a cross.
Corner,  Derby County. Conceded by Atdhe Nuhiu.
Corner,  Derby County. Conceded by Kieran Lee.
Attempt blocked. Jacob Butterfield (Derby County) left footed shot from outside the box is blocked. Assisted by Matej Vydra.
Substitution, Derby County. Ikechi Anya replaces Tom Ince.
Attempt missed. Cyrus Christie (Derby County) header from the centre of the box is too high. Assisted by Tom Ince with a cross following a corner.
Corner,  Derby County. Conceded by Cameron Dawson.
Attempt saved. Jacob Butterfield (Derby County) right footed shot from the centre of the box is saved in the bottom right corner.
Foul by Atdhe Nuhiu (Sheffield Wednesday).
Bradley Johnson (Derby County) wins a free kick in the defensive half.
Offside, Derby County. Cyrus Christie tries a through ball, but Tom Ince is caught offside.
Substitution, Derby County. Matej Vydra replaces Darren Bent.
Attempt missed. Atdhe Nuhiu (Sheffield Wednesday) header from the centre of the box misses to the right. Assisted by Barry Bannan.
Tom Ince (Derby County) is shown the yellow card.
Adam Reach (Sheffield Wednesday) wins a free kick on the left wing.
Foul by Tom Ince (Derby County).
Corner,  Sheffield Wednesday. Conceded by Scott Carson.
Attempt saved. Fernando Forestieri (Sheffield Wednesday) right footed shot from the left side of the box is saved in the centre of the goal. Assisted by Atdhe Nuhiu with a headed pass.
Substitution, Sheffield Wednesday. Atdhe Nuhiu replaces Steven Fletcher because of an injury.
Delay over. They are ready to continue.
Delay in match Steven Fletcher (Sheffield Wednesday) because of an injury.
Attempt missed. Bradley Johnson (Derby County) header from the centre of the box is close, but misses the top left corner. Assisted by Markus Olsson with a cross.
Substitution, Sheffield Wednesday. Ross Wallace replaces David Jones.
Delay over. They are ready to continue.
Delay in match Steven Fletcher (Sheffield Wednesday) because of an injury.
Attempt missed. Darren Bent (Derby County) header from the centre of the box misses to the left. Assisted by Johnny Russell with a cross following a corner.
Corner,  Derby County. Conceded by David Jones.
Goal!  Derby County 2, Sheffield Wednesday 0. Alex Pearce (Derby County) left footed shot from the centre of the box to the bottom left corner following a set piece situation.
Cyrus Christie scored his first goal of the season to help Derby beat Sheffield Wednesday and extend their unbeaten run against the Owls to 17 matches.