Gordon put the Fire on top in the 29th minute as he ran to the far post and jumped over San Jose defender Jimmy Ockford to head Luis Solignac's cross from the right sideline past Earthquakes goalkeeper Andrew Tarbell. Johan Kappelhof also received credit for an assist on the goal.
Katai added to Chicago's lead four minutes into the second half, taking a nifty pass from Brandt Bronico on the head run to beat Earthquakes forward Florian Jungwirth into the box before lobbing a shot over the head of the hard-charging Tarbell and into the far side of the net.
Gordon and Solignac had great chances to add to the lead in the 57th minute, but each player had shots cleared off the line by San Jose defenders after they got past Tarbell.
San Jose cut the Fire's advantage in half in the 74th minute when Danny Hoesen rushed into the zone to receive a pass from Chris Wondolowski and boot it into the goal, as Chicago keeper Richard Sanchez had no chance to respond.
Katai had a chance to ice the match in the 85th minute, but his hard shot from inside the 18-yard line was parried wide by Tarbell.
San Jose has won just once away from home in eight matches in 2018 and has just one victory in its past 12 outings. The Earthquakes dropped their third straight game and extended their winless streak to four matches.
The Earthquakes outshot Chicago 14-13 and each team had four shots on target. San Jose also earned advantages in blocked shots (6-3), crosses (25-10), total passes (481-433), possession (53 percent to 47 percent) and duels won (51-47), but had little to show for its good work.
San Jose returns home to host LAFC next Saturday while the Fire stay in the Windy City to host New England, also on Saturday.
Chicago 2-1 San Jose: Katai leads Fire- Via MLS
Aleksandar Katai doubled the Fire's lead early in the second half as Chicago handed the Earthquakes another loss.