The World No.1 didn't face a break point in his 6-4, 6-3 second-round win over Marius Copil, and he hopes it's the beginning of a warming trend for a service that has been ice-cold since he took a break from tennis due to an elbow injury before the Miami Open.
After Jack Sock and Gael Monfils bit the dust on Monday, Pouille became the third seed to fail to make it out of the first round, losing 7-6 (7-5), 6-7 (4-7), 6-3.
The pair faced each other in the second round in Spain with Bouchard winning 7-5, 2-6, 6-4 in a competitive and tense match.
Murray will face Borna Coric or the victor of the first-round match between Pierre-Hugues Herbert and Lucas Pouille in the last 16, as he seeks to reach the final for the third year in succession.
"I still think there's a way to go. I don't think I'm playing perfectly just now", said Murray. 'But the most positive thing about tonight was that I feel like I can serve a little bit better than I did today.
The Wimbledon champion passed up two chances to break the Copil serve in the second game of the match.
Murray's conqueror in Barcelona last month and potential quarterfinal opponent Dominic Thiem eased past American Jared Donaldson 6-3, 6-4.
For defending Madrid Open champion Djokovic, the tournament in Spain will also give him a chance to test his game after parting ways with longtime coach Marian Vajda last week.
Ninth seed David Goffin is the only other player to have reached the third round so far, with the majority of the second-round clashes taking place on Wednesday. I don't think I deserved to lose this match. It was a very hard week, last week.
"I've spoken about this at length pretty much for 15 months now", Murray added, as quoted on BBC. However he spoke of how he had the shortest of practices in the main court, and faces Coric who is at least fairly match-sharp here in Madrid having come through a couple of rounds of qualifying before getting his shot at the main draw. He lost to Australia's Nick Kyrgios in the quarter-finals in Acapulco and in the Round of 16 in Indian Wells.
Only three of the top 10 seeds remain as the woman Halep beat in last year's final, Dominika Cibulkova, was swept aside 6-2, 6-4 by 20-year-old Frenchwoman Oceane Dodin.