Idrissa Sylla volleyed the hosts ahead when he reacted quickest to Christophe Berra's poor defensive header.
Tom Lawrence spectacularly equalised early in the second half as he blasted into the top corner from 25 yards.
David McGoldrick, Myles Kenlock and Lawrence had chances to put Ipswich ahead, but Wszolek rounded the keeper and shot home after a defensive error.
QPR, who had lost six in a row before their win at Wolves on New Year's Eve, move up to 17th place in the Championship, two points and two places behind Ipswich.
McGoldrick had two good chances early on for the Suffolk side before Sylla's opener, but Rangers' Guinean striker was forced off with a neck injury soon after giving his side the lead.
Lawrence equalised soon after the restart with an effort that is likely to be a contender for Town's goal of the season, but they missed a series of chances before the home side's winner.
Adam Webster misjudged the flight of a ball over the top and Wszolek took advantage, controlling well before taking it around fellow Pole Bartosz Bialkowski and slotting home.
QPR manager Ian Holloway:
"The window's massive for us and now people have seen us win two games they might actually want to come here instead of thinking 'Do I want to go in to a dressing room like that?'
"No-one likes to have a terrible run like that. It's a horrible feeling and I felt so down, but I never showed the lads because what they were producing at times was quite promising but they were getting nothing."
"Football's about having a balance of legs and knowledge and experience and youth.
"We've also got to see fight here - and we saw that again today. Now I can have a look at things and see what's right for us."
Ipswich Town manager Mick McCarthy:
"We played really well today but we conceded two really bad goals.
"We created a lot of chances and the second half was a great performance, but we didn't manage to score and then we gave away a milky goal.
"It was a good performance all round, but they put it in the net instead of us. It should have been a 1-1 draw and if we don't win that game then there's no way we should lose it."
Match ends, Queens Park Rangers 2, Ipswich Town 1.
Second Half ends, Queens Park Rangers 2, Ipswich Town 1.
Attempt saved. David McGoldrick (Ipswich Town) left footed shot from the right side of the box is saved in the centre of the goal. Assisted by Luke Chambers.
Foul by Christophe Berra (Ipswich Town).
Nedum Onuoha (Queens Park Rangers) wins a free kick in the defensive half.
Cole Skuse (Ipswich Town) wins a free kick in the attacking half.
Foul by Jordan Cousins (Queens Park Rangers).
Corner,  Queens Park Rangers. Conceded by Jonathan Douglas.
Foul by Christophe Berra (Ipswich Town).
Joel Lynch (Queens Park Rangers) wins a free kick in the defensive half.
Grant Ward (Ipswich Town) wins a free kick in the defensive half.
Foul by Jordan Cousins (Queens Park Rangers).
Goal!  Queens Park Rangers 2, Ipswich Town 1. Pawel Wszolek (Queens Park Rangers) right footed shot from the right side of the six yard box to the centre of the goal. Assisted by Nedum Onuoha with a through ball.
Attempt missed. David McGoldrick (Ipswich Town) left footed shot from the centre of the box is too high. Assisted by Tom Lawrence.
Jonas Knudsen (Ipswich Town) wins a free kick in the defensive half.
Foul by Conor Washington (Queens Park Rangers).
Attempt blocked. Abdenasser El Khayati (Queens Park Rangers) right footed shot from the left side of the box is blocked. Assisted by Jake Bidwell.
Attempt missed. Tom Lawrence (Ipswich Town) left footed shot from the left side of the box misses to the left. Assisted by David McGoldrick.
Substitution, Ipswich Town. Jonas Knudsen replaces Myles Kenlock.
Grant Ward (Ipswich Town) wins a free kick on the right wing.
Foul by Jake Bidwell (Queens Park Rangers).
Foul by David McGoldrick (Ipswich Town).
Pawel Wszolek (Queens Park Rangers) wins a free kick in the defensive half.
Tom Lawrence (Ipswich Town) wins a free kick in the attacking half.
Foul by James Perch (Queens Park Rangers).
Foul by Myles Kenlock (Ipswich Town).
Pawel Wszolek (Queens Park Rangers) wins a free kick in the defensive half.
Substitution, Queens Park Rangers. Abdenasser El Khayati replaces Ryan Manning.
Substitution, Ipswich Town. Jonathan Douglas replaces Kevin Bru.
Corner,  Ipswich Town. Conceded by Grant Hall.
Attempt blocked. Tom Lawrence (Ipswich Town) right footed shot from the right side of the box is blocked. Assisted by Grant Ward.
Corner,  Ipswich Town. Conceded by Alex Smithies.
Attempt saved. Myles Kenlock (Ipswich Town) left footed shot from the left side of the six yard box is saved in the bottom left corner. Assisted by Tom Lawrence.
Foul by Tom Lawrence (Ipswich Town).
James Perch (Queens Park Rangers) wins a free kick in the defensive half.
Attempt missed. Ryan Manning (Queens Park Rangers) left footed shot from outside the box misses to the right following a corner.
Corner,  Queens Park Rangers. Conceded by Myles Kenlock.
Foul by Myles Kenlock (Ipswich Town).
James Perch (Queens Park Rangers) wins a free kick in the defensive half.
Substitution, Queens Park Rangers. Nedum Onuoha replaces Ariel Borysiuk.
Pawel Wszolek's late winner saw Ian Holloway win back-to-back games for the first time since taking over at QPR.