The Reds led twice in the first half but Ipswich, beaten 1-0 by Wrexham in the FA Cup fourth round last weekend, made it 2-2 at the break before going 3-2 up at the start of the second period.
However, Phil Parkinson’s men scored three times to secure a brilliant win.
Top scorer Kieffer Moore, with his first goal since Boxing Day and 13th of the season, and Josh Windass – up to 10 for the campaign – struck in the first 45 minutes.
George Thomason, Callum Doyle and Nathan Broadhead then found the back of the net in the second half as Wrexham climbed up to sixth place in the table.
There are 13 games remaining in the quest for a play-off spot with Wrexham back in action at home to Portsmouth on Tuesday.
Parkinson made two changes from the side that drew 2-2 against Bristol City on Tuesday, and he also switched to a 3-5-2 formation.
Windass took over from Broadhead and he played off striker Moore who replaced Sam Smith, with Ben Sheaf, Lewis O’Brien and Ollie Rathbone lining up in midfield.
Wrexham went straight at Ipswich and the good start paid off with the Reds going ahead in the sixth minute.
Windass headed the ball onto Moore who ran at goal and fired an unstoppable shot past keeper Christian Walton from a tight angle.
Ivan Azon saw a header comfortably saved by Arthur Okonkwo with Ipswich’s first sight of goal before Wrexham lost Sheaf to injury, with George Dobson coming on in midfielder.
But Ipswich equalised on 20 minutes.
Jack Taylor ran at goal and his low drive was parried by Okonkwo with Anis Mehmeti firing into the roof of the net from Azon’s lay-off.
Wrexham began losing possession carelessly but they reclaimed the lead after 37 minutes following a good move.
Thomason’s shot was saved by Walton, Moore put ball back into the danger zone and Windass found the net with a header despite the best efforts of Leif Davis who was shown a yellow card for handing the ball on the line.
Wrexham continued to press and Moore was denied by Walton following Thomason’s cross and Doyle headed wide from Rathbone’s cross.
But Ipswich equalised in the third minute of added time.
Azor Matusiwa’s pass found Taylor who laid the ball off for Azon to leave the Wrexham defence carved open and the striker fired past Okonkwo to leave it all-square at the break.
It remained 2-2 at the break but Ipswich went ahead for the first time just two minutes into the second half.
A cross was partially cleared by Dobson and Cedric Kipre found the net with a superb drive from the edge of the area.
Wrexham responded with Windass playing a superb through-ball to Thomason whose shot was tipped behind by Walton.
And from the resulting corner which wasn’t cleared, Doyle was taken out by Walton, although a penalty wasn’t given.
However, Wrexham equalised in the 66th minute.
Broadhead ran at goal and although his shot was blocked by a defender, Thomason found the net for his first Wrexham goal.
Buoyed by the goal, Broadhead’s drive was gathered by Walton and Wrexham went 4-3 up after 75 minutes.
O’Brien sent in a corner and Doyle rose highest to head past Walton.
Doyle was needed at the other end to head the ball clear to keep out Marcelino Nunez’s goal-bound effort before Windass was denied by Walton at the other end..
But Wrexham made it 5-3 four minutes from time.
O’Brien picked out Broadhead with a brilliant pass and the winger fired past Walton from inside the area to complete the scoring and secure a brilliant win.
Wrexham (3-5-2): Okonkwo; Cleworth, Hyam, Doyle; Kabore (Longman 64), Sheaf (Dobson 16), O’Brien, Rathbone (Broadhead 64), Thomason; Windass (Vyner 85), Moore. Subs not used: Ward, Scarr, Keilor-Dunn, Cadamarteri, Smith
Ipswich (4-2-3-1): Walton; Furlong, O’Shea, Kipre, Davis; Matusiwa (Akpom 80), Taylor (Neil 70); Burns (McAteer 70), Mehmeti (Nunez 70), Clarke; Azón (Hirst 76). Subs not used: Palmer, Walle Egeli, Cajuste, Greaves.
Attendance: 10,610 (1,288 from Ipswich).