Everton secured their second win in nine games on a comfortable afternoon against Palace at Goodison Park.
Playing only his 2nd game since returning from a 10-month injury layoff due to a double fracture, Coleman appeared to have suffered a muscle injury, leading to his withdrawal at the start of the 2nd half.
Sam Allardyce says it is time for Everton to improve on their poor away form.
After a goalless first-half, Everton eventually broke the deadlock thanks to Sigurdsson whose low shot from the edge of Palace's box took a slight deflection off a defender before beating Wayne Hennessey in goal.
"Rhino" took temporary charge of first-team affairs in October after the sacking of Ronald Koeman and stated his desire to secure the job on a full-time basis, only for a awful run as caretaker that saw Everton win only two of eight matches to scupper those hopes.
Tom Davies added a third before a late Palace penalty wiped out Everton's clean sheet, but they held on for a good three points.
There was also late drama at the Liberty Stadium where Ki Sung-yueng struck the victor as Swansea continued their resurgence under Carlos Carvalhal by beating out-of-form Burnley 1-0.
The win leaves the two sides level on 30 points apiece in the middle of the table, though still just six points above the relegation zone.
Another game without a goal means that the 27-year-old has now scored just twice in 21 appearances in the Premier League for Palace this season.
Shaqiri then levelled the score with a wonderful individual effort from range, while Charlie Adam failed to convert a penalty in the first minute of second-half stoppage time.
Elsewhere, West Ham moved level on points with 11th-placed Watford by beating the Hornets 2-0 at the London Stadium.