Lincoln had a flying start at Sincil Bank, with Harry Anderson on target within the opening minute.
The blues responded well with Lucas Digne equalizing through a sensational long-range free kick, before Gylfi Sigurdsson deservedly put Marco Silva’s men ahead from the penalty spot.
But Lincoln leveled the scores again thanks to a cracking Bruno Andrade effort 20 minutes from time.
Late headers from Iwobi and Richarlison within the final quarter of an hour ensured the Blues’ progress, however.
The Nigeria international celebrated his goal enthusiastically with his teammates and revealed after the game that he is confident his strike will be the first of many special moments he will experience in an Everton shirt.
— Everton (@Everton) August 29, 2019
“I am enjoying my time here, it is a new chapter in my life,”
“I am so happy and there are more memories to come.
“It was a difficult game and we have to give credit to Lincoln”
“But the most important thing is we are through to the next round.
“We showed we have that fighting spirit, and that’s good to see” said the 23-year-old former Arsenal winger.
Everton will face Sheffield Wednesday at Hillsborough in the third round of the Carabao Cup on the week commencing 23 September.