Cyriel Dessers, on target as he rescued a draw for Rangers in their Champions League qualifier against Dynamo Kyiv in Poland on Tuesday, opened the scoring in the 13th minute before Gers debutant Robin Propper scored an own-goal four minutes later.
But winger Vaclav Cerny, making his first Rangers start since signing on loan from Bundesliga club Wolfsburg, restored the Glasgow giants' lead in the 24th minute with a fine finish from the edge of the box.
Rangers, however, were a more subdued side in the second half and they allowed Motherwell back into the game to set up a tense finish.
This was the first of four games Rangers are playing at Hampden while a delayed refurbishment of their own Ibrox ground is completed and they will return to Scotland's national football stadium on Tuesday for the second leg of their European tie with Dynamo Kyiv.
"We will need a good efficiency (against Kyiv)," said Rangers manager Philippe Clement. "You will not get 19 shots like today, or nine on target like today.
"We need to be really efficient in that game. And it's a team that showed a lot of quality the last couple of weeks.
"The last couple of years also, by playing together, so we need to be on top of our game."
The Belgian added: "And then to have the 50,000 behind us to push us through the difficult moments. It's always been crucial at Ibrox, and now it's important we get it at Hampden also."
Ross County needed a late equaliser from Ronan Hale to secure a 1-1 draw at home to Dundee United.
David Babunski had put United ahead after linking up well with fellow new signing Will Ferry, but Hale stepped up five minutes into stoppage time to secure a draw after County missed a first-half chance when Eamonn Brophy's penalty was saved by Jack Walton.
Saturday's final kick-off saw Dundee post their first Premiership win of the season with a 3-1 victory over Hearts.
Scott Tiffoney's early opener, Gerald Taylor's own goal and a Luke McCowan penalty put Dundee 3-0 in front at half-time, with Frankie Kent pulling a goal back just after the hour.
Reigning champions Celtic start Sunday's fixtures away to Hibernian, before Aberdeen welcome St Mirren and Kilmarnock face St Johnstone.
