Home goalkeeper David Martin pulled off an instinctive stop to halt a shot by Kallum Higginbotham on 32 minutes, but was powerless to stop Scotland forward Rhodes from glancing a header into the net from Lee Novak's cross seconds later for his 38th goal of the campaign.
MK Dons huffed and puffed without ever looking likely to blow down a visiting side who were content to sit deep and play on the break.
Huddersfield keeper Ian Bennett spread himself superbly well to halt an effort from Dean Lewington just after half-time, but Bennett was largely a spectator for most of the match.
The visiting side added what could yet prove to be a killer second in the overall tie when Jack Hunt danced into the home box before thrashing a shot beyond Martin on 73 minutes after some neat attacking play by Higginbotham. It was his third of the season.
Lee Novak drilled a shot wide of goal midway through the second half when he should have netted from Rhodes's headed flick as Simon Grayson's side continued to hit on the counter-attack with some effect.
Bennett clawed out a shot by home substitute Jabo Ibehre deep into seven minutes of time added on as it became clear Karl Robinson's side were not going to find a goal on the day.
Robinson was also furious with the fourth official for giving Novak permission to race back onto play seconds after he had needed treatment on the side of the park for cramp.
Hunt added the second goal moments later, but MK can have no complaints about the result. The one downside for the visiting side was injuries to Scott Arfield and Callum Woods. It remains unclear whether either player will be fit to return for the second leg.
MK Dons need a two-goal win at Huddersfield's Galpharm Stadium on Tuesday to keep alive their hopes of reaching the Championship for the first time since the club was founded in 2004.
Barring an unlikely collapse, Huddersfield look likely to return to the play-off final a year after they lost 3-0 to Peterborough.