Michail Antonio opened the scoring after just 46 seconds when Jarrod Bowen played a low cross into the box from the right of the penalty area, and the striker swept his shot past goalkeeper Arijanet Muric.
The visitors were back on level terms after just six minutes when Liam Delap collected the ball in the box on the left following Dara O'Shea's flick on from a corner, and though he was forced backwards he managed to turn to face the goal and his fierce shot was enough to beat Alphonse Areola.
However, Mohammed Kudus restored West Ham's lead in the 43rd minute when he reacted quickest and headed home from close range after Antonio's header hit the underside of the crossbar and bounced up.
Jarrod Bowen gave Lopetegui's side a 3-1 lead shortly after the half-time interval following errors in the Ipswich backline from Ben Johnson and Muric when he weaved into the penalty area from the right.
Lucas Paqueta scored his side's fourth of the game in the 69th minute after good work from Bowen, who drove into the box from the right and played a pass towards Antonio, but the ball ended up at Paqueta's feet from just yards out and the Brazilian tapped home into an empty net.
The result means that West Ham now 12th with eight points after seven matchweeks and are five points clear of 18th-placed Crystal Palace.
Meanwhile, Ipswich end the day in 17th place with just four points from seven games and are above the relegation zone by just one point.
WEST HAM UNITED VS. IPSWICH TOWN HIGHLIGHTS
Michail Antonio goal vs. Crystal Palace (1st min, West Ham United 1-0 Ipswich Town)
West Ham work the ball to Jarrod Bowen in Ipswich's half on the right side of the pitch, and the Englishman picks out Michail Antonio with a low cross near the edge of the box and the striker sweeps the ball past goalkeeper Arijanet Muric.
Antonio scores after just 46 seconds!
Liam Delap goal vs. Ipswich Town (6th min, West Ham United 1-1 Ipswich Town)
Liam Delap collects the ball in the box after Dara O'Shea's flick on and manages to turn to face the goal before he strikes powerfully towards the bottom-left corner, though Alphonse Areola could do better with his save.
Two goals after just six minutes!
Mohammed Kudus goal vs. Ipswich Town (43rd min, West Ham United 2-1 Ipswich Town)
Mohammed Kudus leaps up and reacts fastest to head home from close range after Antonio hit the underside of the crossbar following Lucas Paqueta's cross into the box from the left.
Kudus scores his first goal of the season!
Jarrod Bowen goal vs. Ipswich Town (49th min, West Ham United 3-1 Ipswich Town)
Ipswich right-back Ben Johnson lobs a pass to goalkeeper Muric, who fails to control the ball and Antonio nearly steals the possession from under his nose, but the ball bounces to Jarrod Bowen and he weaves his way into the penalty area from the right and drills the ball into the bottom-left corner.
What a poor goal to concede from Ipswich!
Lucas Paqueta goal vs. Ipswich Town (69th min, West Ham United 4-1 Ipswich Town)
Lucas Paqueta taps home into an empty net from yards out after Bowen drives into the penalty area from the right and plays a pass towards Antonio, but the ball ends up at Paqueta's feet.
The Brazilian could hardly miss!
MAN OF THE MATCH - JARROD BOWEN
The West Ham forward was once again pivotal for West Ham, assisting his side's first goal, scoring their third and playing a key role in their fourth.
Bowen also created five chances during the course of the game, the most of any player on the pitch.
WEST HAM UNITED VS. IPSWICH TOWN STATS
Possession: West Ham United 55%-45% Ipswich Town
Shots: West Ham United 22-8 Ipswich Town
Shots on target: West Ham United 13-2 Ipswich Town
Corners: West Ham United 5-5 Ipswich Town
Fouls: West Ham United 12-6 Ipswich Town
BEST STATS
WHAT NEXT?
When West Ham return from the international break, they will first face Tottenham Hotspur on October 19 before taking on Manchester United on October 27.
Ipswich arguably have three more favourable fixtures in their next three league games given they play Everton on October 19, followed by matches against Brentford and Leicester City.