The 49ers are banged up and out of playoff position in the NFC, but they found reason to smile on Sunday.

Brock Purdy threw two touchdowns, Isaac Guerendo ran for two more and the defense pitched a shutout in the first half of a 38-13 home win over the Bears. The win moves the 49ers to 6-7 on the season and keeps some hope alive that they may be able to climb back into position to return to the postseason.

Purdy started the scoring with a seven-yard strike to wide receiver Jauan Jennings on the opening possession of the game and he’d find Jennings again to make it 21-0 in the second quarter. Guerendo’s first touchdown came in between the two Jennings scores and his second came after the Bears briefly threatened to make it a game in the third quarter.

After getting the kickoff to start the third quarter, the Bears used a nine-minute drive to get in position for a Caleb Williams touchdown pass to wide receiver Rome Odunze. They forced a three-and-out on the next 49ers possession and drove into enemy territory again, but Williams threw a backward pass while trying to pull the ball back in and the 49ers recovered to set up the second Guerendo score.

Guerendo left with a foot injury, but picked up 128 yards from scrimmage in his first start. Purdy finished 20-of-25 for 325 yards and connected with tight end George Kittle for several big gains. Kittle only had one catch in the Week 13 loss to the Bills, but he rebounded with six grabs for 151 yards on Sunday. Jennings had seven catches for 90 yards and the 49ers rolled up 452 yards overall.

49ers guard Ben Bartch also left the game with an ankle injury, so the injury issues show no sign of subsiding even if the three-game losing streak came to an end.

The Bears only had four yards at halftime, so their third quarter success was heartening even if it was short lived. Williams ended the day 17-of-23 for 134 yards and another touchdown to Odunze, but he was also sacked seven times and has now been dropped 56 times on the year. The NFL record for a single season is 76, so there’s a chance that David Carr will be knocked out of the record book before the year is over.

The 4-9 Bears will be in Minnesota to try to avoid adding to that total next Sunday. The 49ers will stay at home for a Thursday night date with a Rams team that put on an offensive display of its own on Sunday.